title: White torture

text: A 2004 Amnesty International report documented the use of white torture on Amir Fakhravar by the Revolutionary Guards, the first known example of white torture in Iran It states that "his cells had no windows, and the walls and his clothes were white. His meals consisted of white rice on white plates. To use the toilet, he had to put a white piece of paper under the door. He was forbidden to speak, and the guards reportedly wore shoes that muffled sound". Upon his arrival in the US, Fakhravar confirmed this report in an interview with Christian Broadcasting Network.


title: White torture

text: "Since I left Evin, I have not been able to sleep without sleeping pills. It is terrible. The loneliness never leaves you, long after you are 'free.' Every door that is closed on you... This is why we call it 'white torture.' They get what they want without having to hit you. They know enough about you to control the information that you get: they can make you believe that the president has resigned, that they have your wife, that someone you trust has told them lies about you. You begin to break. And once you break, they have control. And then you begin to confess."


title: White torture

text: "I feel that solitary confinement—which wages war on the soul and mind of a person—can be the most inhuman form of white torture for people like me, who are arrested solely for (defending) citizens' rights. I only hope the day comes when no one is put in solitary confinement [to punish them] for the peaceful expression of his ideas."


title: White torture

text: On December 20, 2018, Human Rights Watch urged the regime in Iran to investigate and find an explanation for the death of Vahid Sayadi Nasiri, who had been jailed for insulting the Supreme Leader Ali Khamenei. According to his family, Nasiri had been on a hunger strike but was denied medical attention before he died.


title: White torture

text: The United States has been accused by Amnesty International and other international human rights organizations of using "extreme isolation and sensory deprivation... detainees confined to windowless cells... days without seeing daylight" along with other torture techniques with the approval of the George W. Bush administration under the euphemism "enhanced interrogation." The organization of European Democratic Lawyers (EDL) has explicitly accused the United States of white torture: "Fundamental rights are violated on the part of the United States. In Guantánamo, prisoners are held under sensory deprivation, ears and eyes covered, hands and feet tied, hands in thick gloves, held in cages without any privacy, always observed, light day and night: This is called white torture." Rainer Mausfeld has criticized the practice.


title: White torture

text: According to human rights organizations and other NGOs, the Bolivarian Intelligence Service (SEBIN) of the Venezuelan government holds political prisoners in the lower levels of SEBIN's headquarters, which has been deemed by government officials "The Tomb". The cells are with a cement bed, white walls, and security barriers between one another so that there is no interaction between prisoners. Such conditions have caused prisoners to become very ill, but they are denied medical treatment. Bright lights in the cells are kept on so prisoners lose their sense of time and the temperature is below freezing, with the only sounds heard being from the nearby Caracas Metro trains. Reports of torture in La Tumba, specifically white torture, are also common, with some prisoners attempting to commit suicide. Such conditions according to the NGO Justice and Process are to make prisoners plead guilty to the crimes that they are accused of.


title: Alexandra Billings

text: Alexandra Scott Billings (born March 28, 1962) is an American actress, teacher, and singer. Billings is the second openly transgender woman to have played a transgender character on television, which she did in the 2005 made-for-TV movie "". She is also known for portraying the recurring character Davina in the Amazon series "Transparent" and has played transgender characters in "ER", "Eli Stone", "How to Get Away with Murder", "Grey's Anatomy" and "The Conners".


title: Alexandra Billings

text: Billings was born in Illinois into a multiracial family; she is of European American, African American, and Native American ancestry. Billings' father, Robert Billings, was a music teacher at Los Angeles Harbor College and the musical director for the Los Angeles Civic Light Opera, which influenced her interest in theater. She assisted, working backstage with Carol Burnett and Yul Brynner. She also appeared in "Jesus Christ Superstar" and "The Roar of the Greasepaint—the Smell of the Crowd". In her early adult life, Billings struggled with homelessness and cocaine and opioid addiction, and for a time participated in sex work.


title: Alexandra Billings

text: In the early 1980s, Billings worked under the stage name Shanté at the famed Baton Show Lounge in Chicago, Illinois, where she impersonated Barbra Streisand, Judy Garland, and Liza Minnelli. Winning a series of beauty contests, she was named Miss Wisconsin, Miss New York, Miss Chicago, Miss Illinois, and Miss Florida. She also served as a judge of the Miss Continental pageant in 2000 and 2001.


title: Alexandra Billings

text: Most of Billings' professional work has been in Chicago theaters, most notably The Bailiwick Theater, Light Opera Works, Court Theatre, and Steppenwolf Theatre. She has collaborated on plays with such notable authors as Larry Kramer, Tina Landau, and Jamie Pachino. She has received one Joseph Jefferson Award and five After Dark Awards for her work in Chicago Theatre. Her one-person autobiographical show has toured to Boston, Chicago, Los Angeles and off Broadway. She is a former artistic associate of About Face Theatre.


title: Alexandra Billings

text: Billings is also a professional singer who performs in theaters and nightclubs throughout the United States. She recorded her second CD, "The Story Goes On", in 2003. She was a recipient of the New York MAC Hanson Award for Cabaret Artist of the Year in 2004.


title: Alexandra Billings

text: More recently, Billings has appeared in an autobiographical show, "S/He and Me". In fall 2018, she also appeared in "The Nap" at Manhattan Theatre Club, and is one of the first openly trans people to be cast in a trans role on Broadway.


title: Alexandra Billings

text: In September 2019, it was announced that Billings would play the role of Madame Morrible in the Broadway musical "Wicked". She is the first openly transgender person to star in the show. After the closure of Broadway during the COVID-19 pandemic, Billings appeared with several other performers on "Good Morning America" in fall 2021 to announce the return of several shows to Broadway, including "Wicked". As of fall 2021, Billings has resumed performing the role of Morrible.


title: Alexandra Billings

text: In the early 2000s, WTTW, the PBS station in Chicago, produced a documentary about Billings' life and career, "Schoolboy to Showgirl: The Alexandra Billings Story."


title: Alexandra Billings

text: She has appeared in the 2005 made-for-TV movie "Romy and Michelle: A New Beginning". She has also played transgender characters in episodes of "Karen Sisco", "ER", "Eli Stone" and "Grey's Anatomy".


title: Alexandra Billings

text: In 2010, Billings appeared in the film "FAUX", in which she commented on gay marriage spurring the economy.


title: Alexandra Billings

text: In 2015, Billings appeared on season two, episode six of "How to Get Away with Murder" as Professor Jill Hartford.


title: Alexandra Billings

text: In 2017, transgender actors and actresses, including Billings (with the help of GLAAD and ScreenCrush), were part of a film to Hollywood written by Jen Richards, asking for more and improved roles for transgender people.


title: Alexandra Billings

text: Billings may be best known for her role as Davina in the Amazon series "Transparent". The character was introduced in an early episode of season one and appeared throughout the show's run.


title: Alexandra Billings

text: In 2020, Billings appeared in a recurring role as Robin, a transgender supervisor at Wellman Plastics and mentor to Darlene Conner on ABC's "The Conners".


title: Alexandra Billings

text: She had a recurring role as Inspector Ainsley Lowbeer in the 2022 Amazon Prime Video science fiction series "The Peripheral".


title: Alexandra Billings

text: She has taught Viewpoints, a method and approach of theater, at the Steppenwolf Summer School. She also taught at Louis University, The University of Chicago, Illinois University, the Illinois Theatre Convention, Act One Studios, and various classes and workshops around the Chicago area, as well as the Steppenwolf School West in Los Angeles California.


title: Alexandra Billings

text: Billings is a theater professor at the University of Southern California in Los Angeles. Before working at USC, she was an assistant professor at California State University, Long Beach. She received her MFA from CSULB, and delivered the commencement speech for CSULB College of the Arts in 2015.


title: Alexandra Billings

text: Billings is an AIDS and LGBTQ activist and advocate for the equality of the LGBTQ community. She encourages others to use their voices to create change within the LGBTQ community.


title: Alexandra Billings

text: In 2016, Billings was awarded the Human Rights Campaign Visibility Award, which recognizes outstanding members of the LGBTQ community who live openly and freely in the public eye. After receiving the award, Billings thanked the audience, but also said, “I look around and I see you all and I cannot tell you how grateful I am that you’re here, and I have to say something to you - I think you look great, you look swell and it’s wonderful that you’re here eating the chicken - it’s delightful, but I must tell you that we have to do something more than sit and speak and talk to our neighbors and eat great food and put on fancy clothes.”


title: Alexandra Billings

text: In 2017, "Transparent", the hit TV show Billings stars in, won the GLAAD Media Award for Outstanding Comedy Series. When accepting the award on behalf of the cast, Billings urged the audience to talk to people who disagree with their beliefs in order to spark conversation and create change instead of staying complacent. Specifically, she called out the older LGBTQ generation and asks them to guide the younger LGBTQ generation because they will be the ones continuing the fight for equality in the future.


title: Alexandra Billings

text: When delivering the commencement speech to the graduating class of the California State University, Long Beach in 2015, Billings once again emphasized the importance of voice when she told the students that it is their job is to speak loud, big, and wide in order to spread their voices.


title: Alexandra Billings

text: Billings lives in Hollywood, California, with her wife Chrisanne, whom she initially met at age fourteen in drama class. They were married in a commitment ceremony in Chicago on December 4, 1995. Billings was chosen as the Grand Marshal for the Pride Parade in Chicago, Illinois on June 28, 2009.


title: Alexandra Billings

text: Billings started her male to female transition in 1980. She has been living with HIV since 1985, and has been an advocate for HIV health initiatives, as well as trans issues and trans rights. When talking about her fight to battle AIDS, she says that she believes the reason she has survived all these years is because of her wife who stood by her, loved her, and supported her through it all. She has spoken about living with HIV in a number of interviews, including a 2016 article with her hometown paper. She also spoke to "POZ" magazine for a 2003 interview about life with HIV. In 2022, she published her memoir "This Time for Me: A Memoir".


title: Newgrounds

text: Newgrounds is an entertainment website and company founded by Tom Fulp in 1995. It hosts user-generated content such as games, films, audio, and artwork. Fulp produces in-house content at the headquarters and offices in Glenside, Pennsylvania.


title: Newgrounds

text: In the 2000s and 2010s, Newgrounds played an important role in Internet culture, and in Internet animation and independent video gaming in particular. It has been called a "distinct time in gaming history", a place "where many animators and developers cut their teeth and gained a following long before social media was even a thing", and "a haven for fostering the greats of internet animation".


title: Newgrounds

text: User-generated content can be uploaded and categorized into either one of the site's four web portals: Games, Movies, Audio, and Art. A Movie or Games submission entered undergoes the process termed "judgment", where it can be rated by all users (from 0 to 5 stars) and reviewed by other users. The average score calculated at various points during judgment determines if whether the content will be "saved" (added onto the database) or "blammed" (deleted with only its reviews saved in the "Obituaries" section).


title: Newgrounds

text: Since Adobe Flash Player was shut down on most current browsers by late 2020, Newgrounds uses the Ruffle emulator, an Adobe Flash emulator written in Rust and is sponsored by Newgrounds along with other popular sites like Cool Math Games and Armor Games for content created with Flash. As of 2022, Ruffle only supported a select few number of Flash projects written in which meant users had to download the "Newgrounds Player", the site's own Flash emulator which it used prior to Ruffle, to run projects written in AS3.


title: Newgrounds

text: Art and Audio are processed using a different method called "scouting", which the site describes as "a way to vet users and weed out spam, stolen works, low quality submissions, etc." All users can put art and audio onto their own page, but only those that are "scouted" will appear in the public area. Like the judgment system, it stops stolen content, spam, or prohibited material reaching the public area, relying on users and site moderators. Once an individual is scouted, they are given the privilege to scout others, though users caught scouting other users who regularly break the site's terms of service and/or guidelines ("abusing the system") get unscouted themselves.


title: Newgrounds

text: Content and context are liable to be reported for review to the moderators and staff members by flagging it for violations to the site's guidelines. A weighted system recognizes experienced users and gives their flag more voice. Newgrounds' homepage includes featured submissions from each category, as well as awards and honors to users whose submission that fall under the site's requirements to earn them. Members of Newgrounds also organize animations called "collabs" through the discussion forum on the site. Some scholars noted that while hundreds of these "collabs" are produced every year, only 20% are completed due to stress on those making the animations, while other scholars said that animators maintain a "strong sense" of authorship and ownership of what they produce, especially solo animators.


title: Newgrounds

text: Although the site hosted animations about Osama bin Laden, Saddam Hussein, and the Taliban, some scholars argued that the site has had a "relatively balanced" conversation on politics, even though those with right-wing views reflect a "sizable part" of the site's user base.


title: Newgrounds

text: In 1991, at the age 13, Tom Fulp launched a Neo Geo fanzine called "New Ground" and sent issues to approximately 100 members of a club originating on the online service Prodigy. Using a hosting service, he launched a website called "New Ground Remix" in 1995, which increased in popularity during the summer of 1996 after Fulp created the BBS games "Club a Seal" and "Assassin" while a student at Drexel University. He then created "Club a Seal II" and "Assassin II", along with a separate hosting site titled "New Ground Atomix". The 1999 release of "Pico's School", a Flash browser game that "exhibited a complexity of design and polish in presentation that was virtually unseen in amateur Flash game development" of the time helped establish Newgrounds as a "public force."


title: Newgrounds

text: While Macromedia Flash Player was required for Newgrounds in order to play specific games, the site also brought together members who were interested in producing Flash games and gained "considerable online influence" as a result. It subsequently became one of the most "active Flash creator communities in the English-speaking Internet" and served as a place that game developers could begin their careers. Flash was once described by Newgrounds as the "driving force" behind the site. Even so, those on the site had a "low tolerance for poor quality work", referring mainly to humor and storytelling instead of animation quality. Some animators on the site moved to YouTube by the mid-2000s.


title: Newgrounds

text: By November 2008, Newgrounds had over 1.5 million users and over 130,000 animations. This had increased by August 2010, when it was reported that the site had over 2.2 million users and over 180,000 games and animated films, most of which were animations made by only one person, with others collaboratively made by various individuals. It was also said in 2013 that users had created "hundreds of thousands of animated movies and online games".


title: Newgrounds

text: In 2018, Newgrounds began to encourage contributors to submit their games in an HTML5 format rather than Flash. In November and December, it experienced surges of new members originally from Tumblr when that site began restricting adult content after illegal child pornography was found on it, resulting in the Tumblr iOS app being removed from the App Store.


title: Newgrounds

text: In summer 2019, the administration of Newgrounds unveiled the Newgrounds Player, which has been described as a "solution for playing Flash games and movies" hosted on the site.


title: Newgrounds

text: In April 2021, an additional week for the browser game "Friday Night Funkin'" was exclusively released on Newgrounds at the time, causing the site's server to become overloaded after an influx of site traffic.


title: Newgrounds

text: In July 2021, Fulp received the Game Developers Choice Awards Pioneer Award for his contributions to establishing Newgrounds and subsequent work in The Behemoth.


title: Old English Bulldog

text: The Old English Bulldog was compact, broad and muscular, as reflected in the painting "Crib and Rosa". Through John Scott's engraving, this painting became the best-known and most reproduced painting of dogs from that period. As described in the Philo-kuon standard from 1865, the average height was approximately , and they weighed about .


title: Old English Bulldog

text: The English blood sport of bull-baiting allowed for a specialized breed in the form of the Old English Bulldog. The main locations in London for these exhibitions were the Westminster Pit, Beargarden and Old Conduit Fields.


title: Old English Bulldog

text: Historians are fairly confident that the Old English Bulldog is derived from ancient war dogs, such as the old Mastiff or the extinct Alaunt dog. Others believe that the true origin of the breed is not entirely clear. Depictions in old prints show that the variety was without doubt a small Mastiff with a comparatively long head. The word 'Mastiff' was eventually dropped when describing these smaller Mastiffs, as the Mastiff proper was found too slow for bull-baiting.


title: Old English Bulldog

text: Two other recognized members of the breed can be seen in the 1817 painting "Crib and Rosa", with Rosa exemplifying the form and size of the ideal type of Old English Bulldog, albeit deficient in wrinkles about the head and neck and in substance of bone in the limbs.


title: Old English Bulldog

text: Many authors bring us descriptions about the extinct bulldog, but this description by William Hamilton Maxwell stands out as one of the most extensive:


title: Old English Bulldog

text: In England, the passage of the Cruelty to Animals Act 1835 caused a decline of bull-baiting and dog fighting, leading to a lack of interest in perpetuating the Old English Bulldog. Three dogs from the Duke of Hamilton's strain of Old English Bulldog, Wasp, Child, and Billy, were depicted in a painting and recognized as some of the last known members of the breed before it became extinct.


title: Old English Bulldog

text: Despite the laws making dog fighting illegal, it continued for many years. Breeders determined a cross between the Old English Bulldog and Old English Terrier created a superior fighting dog with increased quickness and dexterity. This new breed of dog, called the bull and terrier, was a precursor to the Staffordshire Bull Terrier, Bull Terrier and American Pit Bull Terrier and accelerated the extinction of the Old English Bulldog.


title: Old English Bulldog

text: Often confused with the Old English Bulldog, the English Bulldog is noted for its sweet disposition; it does not have the speed and agility that were the definitive characteristics of the Old English Bulldog.


title: Euler–Lagrange equation

text: In the calculus of variations and classical mechanics, the Euler–Lagrange equations are a system of second-order ordinary differential equations whose solutions are stationary points of the given action functional. The equations were discovered in the 1750s by Swiss mathematician Leonhard Euler and Italian mathematician Joseph-Louis Lagrange.


title: Euler–Lagrange equation

text: Because a differentiable functional is stationary at its local extrema, the Euler–Lagrange equation is useful for solving optimization problems in which, given some functional, one seeks the function minimizing or maximizing it. This is analogous to Fermat's theorem in calculus, stating that at any point where a differentiable function attains a local extremum its derivative is zero.


title: Euler–Lagrange equation

text: In Lagrangian mechanics, according to Hamilton's principle of stationary action, the evolution of a physical system is described by the solutions to the Euler equation for the action of the system. In this context Euler equations are usually called Lagrange equations. In classical mechanics, it is equivalent to Newton's laws of motion; indeed, the Euler-Lagrange equations will produce the same equations as Newton's Laws. This is particularly useful when analyzing systems whose force vectors are particularly complicated. It has the advantage that it takes the same form in any system of generalized coordinates, and it is better suited to generalizations. In classical field theory there is an analogous equation to calculate the dynamics of a field.


title: Euler–Lagrange equation

text: The Euler–Lagrange equation was developed in the 1750s by Euler and Lagrange in connection with their studies of the tautochrone problem. This is the problem of determining a curve on which a weighted particle will fall to a fixed point in a fixed amount of time, independent of the starting point.


title: Euler–Lagrange equation

text: Lagrange solved this problem in 1755 and sent the solution to Euler. Both further developed Lagrange's method and applied it to mechanics, which led to the formulation of Lagrangian mechanics. Their correspondence ultimately led to the calculus of variations, a term coined by Euler himself in 1766.


title: Euler–Lagrange equation

text: Let formula_1 be a mechanical system with formula_2 degrees of freedom. Here formula_3 is the configuration space and formula_4 the "Lagrangian", i.e. a smooth real-valued function such that formula_5 and formula_6 is an formula_2-dimensional "vector of speed". (For those familiar with differential geometry, formula_3 is a smooth manifold, and formula_9 where formula_10 is the tangent bundle of formula_11


title: Euler–Lagrange equation

text: Let formula_12 be the set of smooth paths formula_13 for which formula_14 and formula_15 The action functional formula_16 is defined via


title: Euler–Lagrange equation

text: The left hand side of the previous equation is the functional derivative formula_29 of the functional formula_30. A necessary condition for a differentiable functional to have an extremum on some function is that its functional derivative at that function vanishes, which is granted by the last equation.


title: Euler–Lagrange equation

text: A standard example is finding the real-valued function "y"("x") on the interval ["a", "b"], such that "y"("a") = "c" and "y"("b") = "d", for which the path length along the curve traced by "y" is as short as possible.


title: Euler–Lagrange equation

text: under fixed boundary conditions for the function itself as well as for the first formula_36 derivatives (i.e. for all formula_37). The endpoint values of the highest derivative formula_38 remain flexible.


title: Euler–Lagrange equation

text: If the problem involves finding several functions (formula_39) of a single independent variable (formula_40) that define an extremum of the functional


title: Euler–Lagrange equation

text: A multi-dimensional generalization comes from considering a function on n variables. If formula_43 is some surface, then


title: Euler–Lagrange equation

text: When "n" = 2 and functional formula_46 is the energy functional, this leads to the soap-film minimal surface problem.


title: Euler–Lagrange equation

text: If there is a single unknown function "f" to be determined that is dependent on two variables "x" and "x" and if the functional depends on higher derivatives of "f" up to "n"-th order such that


title: Euler–Lagrange equation

text: wherein formula_52 are indices that span the number of variables, that is, here they go from 1 to 2. Here summation over the formula_52 indices is only over formula_54 in order to avoid counting the same partial derivative multiple times, for example formula_55 appears only once in the previous equation.


title: Euler–Lagrange equation

text: If there are "p" unknown functions "f" to be determined that are dependent on "m" variables "x" ... "x" and if the functional depends on higher derivatives of the "f" up to "n"-th order such that


title: Euler–Lagrange equation

text: where formula_52 are indices that span the number of variables, that is they go from 1 to m. Then the Euler–Lagrange equation is


title: Euler–Lagrange equation

text: where the summation over the formula_52 is avoiding counting the same derivative formula_60 several times, just as in the previous subsection. This can be expressed more compactly as


title: Euler–Lagrange equation

text: Let formula_62 be a smooth manifold, and let formula_63 denote the space of smooth functions formula_64. Then, for functionals formula_65 of the form


title: Euler–Lagrange equation

text: where formula_67 is the Lagrangian, the statement formula_68 is equivalent to the statement that, for all formula_69, each coordinate frame trivialization formula_70 of a neighborhood of formula_71 yields the following formula_72 equations:


title: Polyhedron

text: In geometry, a polyhedron (plural polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices.


title: Polyhedron

text: A convex polyhedron is the convex hull of finitely many points, not all on the same plane. Cubes and pyramids are examples of convex polyhedra.


title: Polyhedron

text: A polyhedron is a 3-dimensional example of a polytope, a more general concept in any number of dimensions.


title: Polyhedron

text: Convex polyhedra are well-defined, with several equivalent standard definitions. However, the formal mathematical definition of polyhedra that are not required to be convex has been problematic.


title: Polyhedron

text: Many definitions of "polyhedron" have been given within particular contexts, some more rigorous than others, and there is not universal agreement over which of these to choose.


title: Polyhedron

text: Some of these definitions exclude shapes that have often been counted as polyhedra (such as the self-crossing polyhedra) or include


title: Polyhedron

text: shapes that are often not considered as valid polyhedra (such as solids whose boundaries are not manifolds). As Branko Grünbaum observed,


title: Polyhedron

text: Nevertheless, there is general agreement that a polyhedron is a solid or surface that can be described by its vertices (corner points), edges (line segments connecting certain pairs of vertices),


title: Polyhedron

text: faces (two-dimensional polygons), and that it sometimes can be said to have a particular three-dimensional interior volume.


title: Polyhedron

text: One can distinguish among these different definitions according to whether they describe the polyhedron as a solid, whether they describe it as a surface, or whether they describe it more abstractly based on its incidence geometry.


title: Polyhedron

text: In all of these definitions, a polyhedron is typically understood as a three-dimensional example of the more general polytope in any number of dimensions. For example, a polygon has a two-dimensional body and no faces, while a 4-polytope has a four-dimensional body and an additional set of three-dimensional "cells".


title: Polyhedron

text: However, some of the literature on higher-dimensional geometry uses the term "polyhedron" to mean something else: not a three-dimensional polytope, but a shape that is different from a polytope in some way. For instance, some sources define a convex polyhedron to be the intersection of finitely many half-spaces, and a polytope to be a bounded polyhedron. The remainder of this article considers only three-dimensional polyhedra.


title: Polyhedron

text: Polyhedra may be classified and are often named according to the number of faces. The naming system is based on Classical Greek, and combines a prefix counting the faces with the suffix "hedron", meaning "base" or "seat" and referring to the faces. For example a tetrahedron is a polyhedron with four faces, a pentahedron is a polyhedron with five faces, a hexahedron is a polyhedron with six faces, etc. For a complete list of the Greek numeral prefixes see , in the column for Greek cardinal numbers. The names of tetrahedra, hexahedra, octahedra (8-sided polyhedra), dodecahedra (12-sided polyhedra), and icosahedra (20-sided polyhedra) are sometimes used without additional qualification to refer to the Platonic solids, and sometimes used to refer more generally to polyhedra with the given number of sides without any assumption of symmetry.


title: Polyhedron

text: Some polyhedra have two distinct sides to their surface. For example, the inside and outside of a convex polyhedron paper model can each be given a different colour (although the inside colour will be hidden from view). These polyhedra are orientable. The same is true for non-convex polyhedra without self-crossings. Some non-convex self-crossing polyhedra can be coloured in the same way but have regions turned "inside out" so that both colours appear on the outside in different places; these are still considered to be orientable. However, for some other self-crossing polyhedra with simple-polygon faces, such as the tetrahemihexahedron, it is not possible to colour the two sides of each face with two different colours so that adjacent faces have consistent colours.


title: Polyhedron

text: In this case the polyhedron is said to be non-orientable. For polyhedra with self-crossing faces, it may not be clear what it means for adjacent faces to be consistently coloured, but for these polyhedra it is still possible to determine whether it is orientable or non-orientable by considering a topological cell complex with the same incidences between its vertices, edges, and faces.


title: Polyhedron

text: A more subtle distinction between polyhedron surfaces is given by their Euler characteristic, which combines the numbers of vertices formula_1, edges formula_2, and faces formula_3 of a polyhedron into a single number formula_4 defined by the formula


title: Polyhedron

text: The same formula is also used for the Euler characteristic of other kinds of topological surfaces. It is an invariant of the surface, meaning that when a single surface is subdivided into vertices, edges, and faces in more than one way, the Euler characteristic will be the same for these subdivisions. For a convex polyhedron, or more generally any simply connected polyhedron with surface a topological sphere, it always equals 2. For more complicated shapes, the Euler characteristic relates to the number of toroidal holes, handles or cross-caps in the surface and will be less than 2.


title: Polyhedron

text: All polyhedra with odd-numbered Euler characteristic are non-orientable. A given figure with even Euler characteristic may or may not be orientable. For example, the one-holed toroid and the Klein bottle both have formula_6, with the first being orientable and the other not.


title: Polyhedron

text: For many (but not all) ways of defining polyhedra, the surface of the polyhedron is required to be a manifold. This means that every edge is part of the boundary of exactly two faces (disallowing shapes like the union of two cubes that meet only along a shared edge) and that every vertex is incident to a single alternating cycle of edges and faces (disallowing shapes like the union of two cubes sharing only a single vertex). For polyhedra defined in these ways, the classification of manifolds implies that the topological type of the surface is completely determined by the combination of its Euler characteristic and orientability. For example, every polyhedron whose surface is an orientable manifold and whose Euler characteristic is 2 must be a topological sphere.


title: Polyhedron

text: A toroidal polyhedron is a polyhedron whose Euler characteristic is less than or equal to 0, or equivalently whose genus is 1 or greater. Topologically, the surfaces of such polyhedra are torus surfaces having one or more holes through the middle.


title: Polyhedron

text: The dual of a convex polyhedron can be obtained by the process of polar reciprocation. Dual polyhedra exist in pairs, and the dual of a dual is just the original polyhedron again. Some polyhedra are self-dual, meaning that the dual of the polyhedron is congruent to the original polyhedron.


title: Polyhedron

text: Abstract polyhedra also have duals, obtained by reversing the partial order defining the polyhedron to obtain its dual or opposite order. These have the same Euler characteristic and orientability as the initial polyhedron. However, this form of duality does not describe the shape of a dual polyhedron, but only its combinatorial structure. For some definitions of non-convex geometric polyhedra, there exist polyhedra whose abstract duals cannot be realized as geometric polyhedra under the same definition.


title: Polyhedron

text: For every vertex one can define a vertex figure, which describes the local structure of the polyhedron around the vertex. Precise definitions vary, but a vertex figure can be thought of as the polygon exposed where a slice through the polyhedron cuts off a corner.


title: Polyhedron

text: The surface area of a polyhedron is the sum of areas of its faces, for definitions of polyhedra for which the area of a face is well-defined.


title: Polyhedron

text: The geodesic distance between any two points on the surface of a polyhedron measures the length of the shortest curve that connects the two points, remaining within the surface. By Alexandrov's uniqueness theorem, every convex polyhedron is uniquely determined by the metric space of geodesic distances on its surface. However, non-convex polyhedra can have the same surface distances as each other, or the same as certain convex polyhedra.


title: Polyhedron

text: Polyhedral solids have an associated quantity called volume that measures how much space they occupy. Simple families of solids may have simple formulas for their volumes; for example, the volumes of pyramids, prisms, and parallelepipeds can easily be expressed in terms of their edge lengths or other coordinates. (See Volume § Volume formulas for a list that includes many of these formulas.)


title: Polyhedron

text: Volumes of more complicated polyhedra may not have simple formulas. Volumes of such polyhedra may be computed by subdividing the polyhedron into smaller pieces (for example, by triangulation). For example, the volume of a regular polyhedron can be computed by dividing it into congruent pyramids, with each pyramid having a face of the polyhedron as its base and the centre of the polyhedron as its apex.


title: Polyhedron

text: In general, it can be derived from the divergence theorem that the volume of a polyhedral solid is given by


title: Polyhedron

text: where the sum is over faces of the polyhedron, is an arbitrary point on face , is the unit vector perpendicular to pointing outside the solid, and the multiplication dot is the dot product. In higher dimensions, volume computation may be challenging, in part because of the difficulty of listing the faces of a convex polyhedron specified only by its vertices, and there exist specialized algorithms to determine the volume in these cases.


title: Polyhedron

text: In two dimensions, the Bolyai–Gerwien theorem asserts that any polygon may be transformed into any other polygon of the same area by cutting it up into finitely many polygonal pieces and rearranging them. The analogous question for polyhedra was the subject of Hilbert's third problem. Max Dehn solved this problem by showing that, unlike in the 2-D case, there exist polyhedra of the same volume that cannot be cut into smaller polyhedra and reassembled into each other. To prove this Dehn discovered another value associated with a polyhedron, the Dehn invariant, such that two polyhedra can only be dissected into each other when they have the same volume and the same Dehn invariant. It was later proven by Sydler that this is the only obstacle to dissection: every two Euclidean polyhedra with the same volumes and Dehn invariants can be cut up and reassembled into each other. The Dehn invariant is not a number, but a vector in an infinite-dimensional vector space, determined from the lengths and dihedral angles of a polyhedron's edges.


title: Polyhedron

text: Another of Hilbert's problems, Hilbert's 18th problem, concerns (among other things) polyhedra that tile space. Every such polyhedron must have Dehn invariant zero. The Dehn invariant has also been connected to flexible polyhedra by the strong bellows theorem, which states that the Dehn invariant of any flexible polyhedron remains invariant as it flexes.


title: Polyhedron

text: A three-dimensional solid is a convex set if it contains every line segment connecting two of its points. A convex polyhedron is a polyhedron that, as a solid, forms a convex set. A convex polyhedron can also be defined as a bounded intersection of finitely many half-spaces, or as the convex hull of finitely many points.


title: Polyhedron

text: Important classes of convex polyhedra include the highly symmetrical Platonic solids, the Archimedean solids and their duals the Catalan solids, and the regular-faced Johnson solids.


title: Polyhedron

text: Many of the most studied polyhedra are highly symmetrical, that is, their appearance is unchanged by some reflection or rotation of space. Each such symmetry may change the location of a given vertex, face, or edge, but the set of all vertices (likewise faces, edges) is unchanged. The collection of symmetries of a polyhedron is called its symmetry group.


title: Polyhedron

text: All the elements that can be superimposed on each other by symmetries are said to form a symmetry orbit. For example, all the faces of a cube lie in one orbit, while all the edges lie in another. If all the elements of a given dimension, say all the faces, lie in the same orbit, the figure is said to be transitive on that orbit. For example, a cube is face-transitive, while a truncated cube has two symmetry orbits of faces.


title: Polyhedron

text: The same abstract structure may support more or less symmetric geometric polyhedra. But where a polyhedral name is given, such as icosidodecahedron, the most symmetrical geometry is almost always implied, unless otherwise stated.


title: Polyhedron

text: There are several types of highly symmetric polyhedron, classified by which kind of element – faces, edges, or vertices – belong to a single symmetry orbit:


title: Polyhedron

text: Some classes of polyhedra have only a single main axis of symmetry. These include the pyramids, bipyramids, trapezohedra, cupolae, as well as the semiregular prisms and antiprisms.


title: Polyhedron

text: Regular polyhedra are the most highly symmetrical. Altogether there are nine regular polyhedra: five convex and four star polyhedra.


title: Polyhedron

text: The five convex examples have been known since antiquity and are called the Platonic solids. These are the triangular pyramid or tetrahedron, cube, octahedron, dodecahedron and icosahedron:


title: Polyhedron

text: There are also four regular star polyhedra, known as the Kepler–Poinsot polyhedra after their discoverers.


title: Polyhedron

text: They may be subdivided into the regular, quasi-regular, or semi-regular, and may be convex or starry.


title: Polyhedron

text: The duals of the uniform polyhedra have irregular faces but are face-transitive, and every vertex figure is a regular polygon. A uniform polyhedron has the same symmetry orbits as its dual, with the faces and vertices simply swapped over. The duals of the convex Archimedean polyhedra are sometimes called the Catalan solids.


title: Polyhedron

text: The uniform polyhedra and their duals are traditionally classified according to their degree of symmetry, and whether they are convex or not.


title: Polyhedron

text: An isohedron is a polyhedron with symmetries acting transitively on its faces. Their topology can be represented by a face configuration. All 5 Platonic solids and 13 Catalan solids are isohedra, as well as the infinite families of trapezohedra and bipyramids. Some isohedra allow geometric variations including concave and self-intersecting forms.


title: Polyhedron

text: Many of the symmetries or point groups in three dimensions are named after polyhedra having the associated symmetry. These include:


title: Polyhedron

text: Those with chiral symmetry do not have reflection symmetry and hence have two enantiomorphous forms which are reflections of each other. Examples include the snub cuboctahedron and snub icosidodecahedron.


title: Polyhedron

text: Besides the regular and uniform polyhedra, there are some other classes which have regular faces but lower overall symmetry.


title: Polyhedron

text: Convex polyhedra where every face is the same kind of regular polygon may be found among three families:


title: Polyhedron

text: The total number of convex polyhedra with equal regular faces is thus ten: the five Platonic solids and the five non-uniform deltahedra. There are infinitely many non-convex examples. Infinite sponge-like examples called infinite skew polyhedra exist in some of these families.


title: Polyhedron

text: Norman Johnson sought which convex non-uniform polyhedra had regular faces, although not necessarily all alike. In 1966, he published a list of 92 such solids, gave them names and numbers, and conjectured that there were no others. Victor Zalgaller proved in 1969 that the list of these Johnson solids was complete.


title: Polyhedron

text: Pyramids include some of the most time-honoured and famous of all polyhedra, such as the four-sided Egyptian pyramids.


title: Polyhedron

text: Stellation of a polyhedron is the process of extending the faces (within their planes) so that they meet to form a new polyhedron.


title: Polyhedron

text: Faceting is the process of removing parts of a polyhedron to create new faces, or facets, without creating any new vertices. A facet of a polyhedron is any polygon whose corners are vertices of the polyhedron, and is not a "face".


title: Polyhedron

text: Stellation and faceting are inverse or reciprocal processes: the dual of some stellation is a faceting of the dual to the original polyhedron.


title: Polyhedron

text: A zonohedron is a convex polyhedron in which every face is a polygon that is symmetric under rotations through 180°. Zonohedra can also be characterized as the Minkowski sums of line segments, and include several important space-filling polyhedra.


title: Polyhedron

text: A space-filling polyhedron packs with copies of itself to fill space. Such a close-packing or space-filling is often called a tessellation of space or a honeycomb. Space-filling polyhedra must have a Dehn invariant equal to zero. Some honeycombs involve more than one kind of polyhedron.


title: Polyhedron

text: A convex polyhedron in which all vertices have integer coordinates is called a lattice polyhedron or integral polyhedron. The Ehrhart polynomial of a lattice polyhedron counts how many points with integer coordinates lie within a scaled copy of the polyhedron, as a function of the scale factor. The study of these polynomials lies at the intersection of combinatorics and commutative algebra. There is a far-reaching equivalence between lattice polyhedra and certain algebraic varieties called toric varieties. This was used by Stanley to prove the Dehn–Sommerville equations for simplicial polytopes.


title: Polyhedron

text: It is possible for some polyhedra to change their overall shape, while keeping the shapes of their faces the same, by varying the angles of their edges. A polyhedron that can do this is called a flexible polyhedron. By Cauchy's rigidity theorem, flexible polyhedra must be non-convex. The volume of a flexible polyhedron must remain constant as it flexes; this result is known as the bellows theorem.


title: Polyhedron

text: A polyhedral compound is made of two or more polyhedra sharing a common centre. Symmetrical compounds often share the same vertices as other well-known polyhedra and may often also be formed by stellation. Some are listed in the list of Wenninger polyhedron models.


title: Polyhedron

text: An orthogonal polyhedron is one all of whose faces meet at right angles, and all of whose edges are parallel to axes of a Cartesian coordinate system. (Jessen's icosahedron provides an example of a polyhedron meeting one but not both of these two conditions.) Aside from the rectangular cuboids, orthogonal polyhedra are nonconvex. They are the 3D analogs of 2D orthogonal polygons, also known as rectilinear polygons. Orthogonal polyhedra are used in computational geometry, where their constrained structure has enabled advances on problems unsolved for arbitrary polyhedra, for example, unfolding the surface of a polyhedron to a polygonal net.


title: Polyhedron

text: Polycubes are a special case of orthogonal polyhedra that can be decomposed into identical cubes, and are three-dimensional analogues of planar polyominoes.


title: Polyhedron

text: Regular maps are flag transitive abstract 2-manifolds and they have been studied already in the nineteenth century.


title: Polyhedron

text: Every convex polyhedron is combinatorially equivalent to an essentially unique canonical polyhedron, a polyhedron which has a midsphere tangent to each of its edges.


title: Polyhedron

text: The name 'polyhedron' has come to be used for a variety of objects having similar structural properties to traditional polyhedra.


title: Polyhedron

text: A classical polyhedral surface has a finite number of faces, joined in pairs along edges. The apeirohedra form a related class of objects with infinitely many faces. Examples of apeirohedra include:


title: Polyhedron

text: There are objects called complex polyhedra, for which the underlying space is a complex Hilbert space rather than real Euclidean space. Precise definitions exist only for the regular complex polyhedra, whose symmetry groups are complex reflection groups. The complex polyhedra are mathematically more closely related to configurations than to real polyhedra.


title: Polyhedron

text: Some fields of study allow polyhedra to have curved faces and edges. Curved faces can allow digonal faces to exist with a positive area.


title: Polyhedron

text: When the surface of a sphere is divided by finitely many great arcs (equivalently, by planes passing through the center of the sphere), the result is called a spherical polyhedron. Many convex polytopes having some degree of symmetry (for example, all the Platonic solids) can be projected onto the surface of a concentric sphere to produce a spherical polyhedron. However, the reverse process is not always possible; some spherical polyhedra (such as the hosohedra) have no flat-faced analogue.


title: Polyhedron

text: If faces are allowed to be concave as well as convex, adjacent faces may be made to meet together with no gap. Some of these curved polyhedra can pack together to fill space. Two important types are:


title: Polyhedron

text: Convex polyhedra can be defined in three-dimensional hyperbolic space in the same way as in Euclidean space, as the convex hulls of finite sets of points.


title: Polyhedron

text: However, in hyperbolic space, it is also possible to consider ideal points as well as the points that lie within the space. An ideal polyhedron is the convex hull of a finite set of ideal points. Its faces are ideal polygons, but its edges are defined by entire hyperbolic lines rather than line segments, and its vertices (the ideal points of which it is the convex hull) do not lie within the hyperbolic space.


title: Polyhedron

text: By forgetting the face structure, any polyhedron gives rise to a graph, called its skeleton, with corresponding vertices and edges. Such figures have a long history: Leonardo da Vinci devised frame models of the regular solids, which he drew for Pacioli's book "Divina Proportione", and similar wire-frame polyhedra appear in M.C. Escher's print "Stars". One highlight of this approach is Steinitz's theorem, which gives a purely graph-theoretic characterization of the skeletons of convex polyhedra: it states that the skeleton of every convex polyhedron is a 3-connected planar graph, and every 3-connected planar graph is the skeleton of some convex polyhedron.


title: Polyhedron

text: An early idea of abstract polyhedra was developed in Branko Grünbaum's study of "hollow-faced polyhedra." Grünbaum defined faces to be cyclically ordered sets of vertices, and allowed them to be skew as well as planar.


title: Polyhedron

text: The graph perspective allows one to apply graph terminology and properties to polyhedra. For example, the tetrahedron and Császár polyhedron are the only known polyhedra whose skeletons are complete graphs (K), and various symmetry restrictions on polyhedra give rise to skeletons that are symmetric graphs.


title: Polyhedron

text: From the latter half of the twentieth century, various mathematical constructs have been found to have properties also present in traditional polyhedra. Rather than confining the term "polyhedron" to describe a three-dimensional polytope, it has been adopted to describe various related but distinct kinds of structure.


title: Polyhedron

text: A polyhedron has been defined as a set of points in real affine (or Euclidean) space of any dimension "n" that has flat sides. It may alternatively be defined as the intersection of finitely many half-spaces. Unlike a conventional polyhedron, it may be bounded or unbounded. In this meaning, a polytope is a bounded polyhedron.


title: Polyhedron

text: Analytically, such a convex polyhedron is expressed as the solution set for a system of linear inequalities. Defining polyhedra in this way provides a geometric perspective for problems in linear programming.


title: Polyhedron

text: A topological polytope is a topological space given along with a specific decomposition into shapes that are topologically equivalent to convex polytopes and that are attached to each other in a regular way.


title: Polyhedron

text: Such a figure is called "simplicial" if each of its regions is a simplex, i.e. in an "n"-dimensional space each region has "n"+1 vertices. The dual of a simplicial polytope is called "simple". Similarly, a widely studied class of polytopes (polyhedra) is that of cubical polyhedra, when the basic building block is an "n"-dimensional cube.


title: Polyhedron

text: An abstract polytope is a partially ordered set (poset) of elements whose partial ordering obeys certain rules of incidence (connectivity) and ranking. The elements of the set correspond to the vertices, edges, faces and so on of the polytope: vertices have rank 0, edges rank 1, etc. with the partially ordered ranking corresponding to the dimensionality of the geometric elements. The empty set, required by set theory, has a rank of −1 and is sometimes said to correspond to the null polytope. An abstract polyhedron is an abstract polytope having the following ranking:


title: Polyhedron

text: Any geometric polyhedron is then said to be a "realization" in real space of the abstract poset as described above.


title: Polyhedron

text: Polyhedra appeared in early architectural forms such as cubes and cuboids, with the earliest four-sided pyramids of ancient Egypt also dating from the Stone Age.


title: Polyhedron

text: The earliest known "written" records of these shapes come from Classical Greek authors, who also gave the first known mathematical description of them. The earlier Greeks were interested primarily in the convex regular polyhedra, which came to be known as the Platonic solids. Pythagoras knew at least three of them, and Theaetetus (circa 417 B. C.) described all five. Eventually, Euclid described their construction in his "Elements". Later, Archimedes expanded his study to the convex uniform polyhedra which now bear his name. His original work is lost and his solids come down to us through Pappus.


title: Polyhedron

text: After the end of the Classical era, scholars in the Islamic civilisation continued to take the Greek knowledge forward (see Mathematics in medieval Islam).


title: Polyhedron

text: As with other areas of Greek thought maintained and enhanced by Islamic scholars, Western interest in polyhedra revived during the Italian Renaissance. Artists constructed skeletal polyhedra, depicting them from life as a part of their investigations into perspective. Several appear in marquetry panels of the period. Piero della Francesca gave the first written description of direct geometrical construction of such perspective views of polyhedra. Leonardo da Vinci made skeletal models of several polyhedra and drew illustrations of them for a book by Pacioli. A painting by an anonymous artist of Pacioli and a pupil depicts a glass rhombicuboctahedron half-filled with water.


title: Polyhedron

text: As the Renaissance spread beyond Italy, later artists such as Wenzel Jamnitzer, Dürer and others also depicted polyhedra of various kinds, many of them novel, in imaginative etchings.


title: Polyhedron

text: For almost 2,000 years, the concept of a polyhedron as a convex solid had remained as developed by the ancient Greek mathematicians.


title: Polyhedron

text: During the Renaissance star forms were discovered. A marble tarsia in the floor of St. Mark's Basilica, Venice, depicts a stellated dodecahedron. Artists such as Wenzel Jamnitzer delighted in depicting novel star-like forms of increasing complexity.


title: Polyhedron

text: Johannes Kepler (1571–1630) used star polygons, typically pentagrams, to build star polyhedra. Some of these figures may have been discovered before Kepler's time, but he was the first to recognize that they could be considered "regular" if one removed the restriction that regular polyhedra must be convex. Later, Louis Poinsot realised that star vertex figures (circuits around each corner) can also be used, and discovered the remaining two regular star polyhedra. Cauchy proved Poinsot's list complete, and Cayley gave them their accepted English names: (Kepler's) the small stellated dodecahedron and great stellated dodecahedron, and (Poinsot's) the great icosahedron and great dodecahedron. Collectively they are called the Kepler–Poinsot polyhedra.


title: Polyhedron

text: The Kepler–Poinsot polyhedra may be constructed from the Platonic solids by a process called stellation. Most stellations are not regular. The study of stellations of the Platonic solids was given a big push by H.S.M. Coxeter and others in 1938, with the now famous paper "The 59 icosahedra".


title: Polyhedron

text: The reciprocal process to stellation is called facetting (or faceting). Every stellation of one polytope is dual, or reciprocal, to some facetting of the dual polytope. The regular star polyhedra can also be obtained by facetting the Platonic solids. listed the simpler facettings of the dodecahedron, and reciprocated them to discover a stellation of the icosahedron that was missing from the set of "59". More have been discovered since, and the story is not yet ended.


title: Polyhedron

text: In 1750 Leonhard Euler for the first time considered the edges of a polyhedron, allowing him to discover his polyhedron formula relating the number of vertices, edges and faces. This signalled the birth of topology, sometimes referred to as "rubber sheet geometry", and Henri Poincaré developed its core ideas around the end of the nineteenth century. This allowed many longstanding issues over what was or was not a polyhedron to be resolved.


title: Polyhedron

text: Max Brückner summarised work on polyhedra to date, including many findings of his own, in his book "Vielecke und Vielflache: Theorie und Geschichte" (Polygons and polyhedra: Theory and History). Published in German in 1900, it remained little known.


title: Polyhedron

text: Meanwhile, the discovery of higher dimensions led to the idea of a polyhedron as a three-dimensional example of the more general polytope.


title: Polyhedron

text: By the early years of the twentieth century, mathematicians had moved on and geometry was little studied. Coxeter's analysis in "The Fifty-Nine Icosahedra" introduced modern ideas from graph theory and combinatorics into the study of polyhedra, signalling a rebirth of interest in geometry.


title: Polyhedron

text: Coxeter himself went on to enumerate the star uniform polyhedra for the first time, to treat tilings of the plane as polyhedra, to discover the regular skew polyhedra and to develop the theory of complex polyhedra first discovered by Shephard in 1952, as well as making fundamental contributions to many other areas of geometry.


title: Polyhedron

text: In the second part of the twentieth century, Grünbaum published important works in two areas. One was in convex polytopes, where he noted a tendency among mathematicians to define a "polyhedron" in different and sometimes incompatible ways to suit the needs of the moment. The other was a series of papers broadening the accepted definition of a polyhedron, for example discovering many new regular polyhedra. At the close of the 20th century these latter ideas merged with other work on incidence complexes to create the modern idea of an abstract polyhedron (as an abstract 3-polytope), notably presented by McMullen and Schulte.


title: Marine One

text: Marine One is the call sign of any United States Marine Corps aircraft carrying the president of the United States. It usually denotes a helicopter operated by Marine Helicopter Squadron One (HMX-1) "Nighthawks", consisting of either the large Sikorsky VH-3D Sea King or the newer, smaller VH-60N "White Hawk". Both helicopters are called "White Tops" because of their livery. Any Marine Corps aircraft carrying the vice president without the president has the call sign Marine Two.


title: Marine One

text: The first use of a helicopter to transport the president was in 1957, when President Dwight D. Eisenhower traveled on a Bell UH-13J Sioux. The president wanted a quick way to reach his summer home, in Pennsylvania. Using Air Force One would have been impractical over such a short distance, and there was no airfield near his home with a paved runway to support fixed-wing aircraft, so Eisenhower instructed his staff to investigate other modes of transport and a Sikorsky UH-34 Seahorse helicopter was commissioned. The early aircraft lacked the amenities of its modern successors, such as air conditioning and an aircraft lavatory for use in flight.


title: Marine One

text: Not long after helicopters for presidential transport were introduced, presidential aides asked the Marine Corps to investigate using the White House South Lawn for landing. There was ample room, and the protocol was established. Until 1976, the Marine Corps shared the responsibility of helicopter transportation for the president with the United States Army. Army helicopters used the call sign Army One while the president was on board.


title: Marine One

text: The VH-3D entered service in 1978. The VH-60N entered service in 1987 and has served alongside the VH-3D. Improvements were made to both models of helicopter after their introduction, to take advantage of technological developments and to meet new mission requirements. By about 2001, it was clear that so much extra weight had been added to the helicopters that mission capability was reduced and few new improvements could be made.


title: Marine One

text: By 2009, there were 11 VH-3Ds and eight VH-60Ns in service for the president and other prominent individuals. On 16 July 2009, Marine One flew with an all-female crew for the first time. This was also the final flight of Major Jennifer Grieves, who was the first woman pilot to fly the president.


title: Marine One

text: As of 2009, Marine One had never had an accident or been attacked. However, in 2006, President George W. Bush boarded Marine One with his departing press secretary, but the helicopter "would not work", so the president left the White House in a car.


title: Marine One

text: The September 11 attacks on the United States led to widespread agreement that the Marine One helicopter fleet needed significant upgrades to its communication, transportation, and security systems, but weight limitations prevented the changes.


title: Marine One

text: In April 2002, the Department of Defense began the VXX program, which assigned the Navy to design new presidential helicopters by 2011. In November 2002, the White House asked the Secretary of Defense to accelerate the development of the new aircraft; the Defense Department said a new helicopter would be ready by the end of 2008, and asked companies bidding on the project to begin development and production simultaneously.


title: Marine One

text: Many specifications for the new aircraft were secret. Industry publications and testimony at congressional briefings revealed that it was to be long, carry 14 passengers, be able to carry several thousand pounds of baggage and gear, and have a range greater than those of the VH-3D and the VH-60N. The helicopter's defenses were to include radar jamming and deception, to ward off anti-aircraft missiles; protection of key electronics against nuclear electromagnetic pulse; and an encrypted telecommunications system and videoconferencing.


title: Marine One

text: The only competitors for the contract were Lockheed Martin and Sikorsky Aircraft. Lockheed joined with AgustaWestland, a British and Italian aircraft company, to offer a version of the AgustaWestland AW101. Sikorsky proposed using its S-92. The Navy awarded the contract to Lockheed Martin in January 2005, to develop and build 28 helicopters. The helicopter was designated VH-71 Kestrel. Five of the initial, less sophisticated version of the VH-71 were due for delivery in 2010, with 23 of the upgraded version due for delivery in 2015. The goal was to retire all VH-3Ds and VH-60Ns along with the five initial VH-71s in 2015, leaving the Marine One fleet with 23 helicopters.


title: Marine One

text: By March 2008, the previously estimated $6.1 billion cost of the 28 helicopters had increased to $11.2 billion. Government officials were surprised to discover that each VH-71 would cost $400 million, more than the cost of one Boeing VC-25 "Air Force One" airplane. Lockheed Martin blamed the Navy for the cost overruns, saying that more than 1,900 extra requirements were added to the project after the contract was signed. The Navy said no extra requirements were added. The company also cited the need to redesign the VH-71 to Navy standards, and an incomplete understanding by the Navy and Lockheed Martin of how much retrofitting the civilian aircraft would need to meet the White House's specifications.


title: Marine One

text: In June 2009, the VH-71 program was canceled because of these cost overruns, which had grown to more than an estimated $13 billion. A Government Accountability Office report issued in March 2011 named three sources of cost overruns. First, asking for development at the same time as production led to extensive retrofitting of models that had just been built. Second, a complete review of the system's requirements was not made until four months after production started, and only then was it discovered that the VH-71's design could not meet the program's needs. Third, the Defense Department and the White House asked for excessive combat and communications capabilities.


title: Marine One

text: Shortly after the program's cancellation, the Marine Corps restarted the program. This time, instead of running development and production concurrently, the Corps created an Initial Capabilities Document (ICD), which more clearly outlined the aircraft's requirements. The Department approved the ICD in August 2009, naming it the VXX Helicopter Replacement Program. In February 2010, the Navy asked private industry for input in an Analysis of Alternatives (AOA) to meet the project's needs. Among the options the Navy suggested was purchasing a single aircraft but developing two versions on it. Another option raised by the AOA was to buy two different aircraft—a "civilian" version, with a bathroom, executive suite, and galley, and a "military" version, with complete command and control capabilities. The AOA drew interest from more than two companies. These included Boeing, which told the press that either its CH-47 Chinook or its Bell Boeing V-22 Osprey could meet the AOA's requirements. Because the AOA contemplated a much longer process of design and production, the Navy said it intended to spend $500 million to keep the VH-3Ds and VH-60s flying. Boeing also said it could adapt the VH-71, if the Navy and Marine Corps wished.


title: Marine One

text: In July 2013, the Department of Defense waived the requirement that companies build prototypes. The Department's analysis showed that the cost of making prototypes was unlikely to generate benefits. The Department said that it was proceeding with VXX development using an in-production aircraft with existing, proven systems. A draft request for proposals was released on 23 November 2012.


title: Marine One

text: By August 2013, all interested companies, including Northrop Grumman–AgustaWestland and Bell–Boeing, had withdrawn from the VXX bidding, except Sikorsky Aircraft. Sikorsky had partnered with Lockheed Martin, and said it intended to use the S-92 as the base aircraft. A new deadline in 2020 was established for the 23-helicopter fleet to be in operation. On 7 May 2014, the Navy awarded Sikorsky Aircraft a $1.24 billion contract to build six presidential helicopters, designated Sikorsky VH-92. A fleet of 21 helicopters is expected to be in service by 2023.


title: Marine One

text: Marine One is the preferred alternative to motorcades, which can be expensive and logistically difficult. The controlled environment of a helicopter is also considered to add a safety factor. The HMX-1 fleet is also used to transport senior Cabinet staff and foreign dignitaries. HMX-1 operates 35 helicopters of four different types as of 2009.


title: Marine One

text: More than 800 Marines supervise the operation of the Marine One fleet, which is based in MCAF Quantico, Virginia, with an additional operating location at Naval Support Facility Anacostia in the District of Columbia, but is more often seen in action on the South Lawn of the White House or at Joint Base Andrews Naval Air Facility in Maryland. At Andrews, the helicopter is sometimes used to connect to Air Force One for longer journeys. Marine One is met on the ground by at least one Marine in full dress uniform (most often two, with one acting as an armed guard). According to a story told by Bruce Babbitt, President Clinton, in his final days of office, while flying over and landing in a remote area near the Grand Canyon, found a Marine waiting on the rock ready to salute him. Marine aviators flying Marine One do not wear regular flight suits during flights, but rather the Marine Blue Dress Charlie uniform.


title: Marine One

text: As a security measure, Marine One always flies in a group of as many as five identical helicopters. One helicopter carries the president, while the others serve as decoys. Upon take-off these helicopters shift in formation to obscure the location of the president. This has been referred to as a "presidential shell game". Marine One is also equipped with standard military anti-missile countermeasures such as flares to counter heat-seeking missiles and chaff to counter radar-guided missiles, as well as AN/ALQ-144A infrared countermeasures. To add to the security of Marine One, every member of HMX-1 is required to pass a Yankee White background check before touching any of the helicopters used for presidential travel.


title: Marine One

text: Marine One is transported via C-17 Globemaster or C-5 Galaxy military transport planes (as is the president's limousine) wherever the president travels within the U.S., as well as overseas. Even if, during a foreign trip, the President does not use Marine One, at least one helicopter is on standby in a hangar of a local airport or air base to depart if need be. At a presidential inauguration, the Marines offer the outgoing president a final flight from the Capitol to Joint Base Andrews.


title: 2022 24 Hours of Le Mans

text: The 90th 24 Hours of Le Mans () was a 24-hour automobile endurance event for Le Mans Hypercar (Hypercar), Le Mans Prototypes (LMP) and Le Mans Grand Touring Endurance (LMGTE) cars which took place on 11 and 12 June 2022 at the Circuit de la Sarthe, near Le Mans, France before 244,200 spectators. It was the 90th edition of the event organised by the Automobile Club de l'Ouest, and the third round of the 2022 FIA World Endurance Championship. A test day was held the week before the race on 5 June.


title: 2022 24 Hours of Le Mans

text: A Toyota GR010 Hybrid shared by Sébastien Buemi, Brendon Hartley and Ryō Hirakawa started from pole position after Hartley recorded the fastest overall lap time in the Hyerpole session. The three drivers led for 274 of the race's 380 laps and finished first, two minutes and 1.222 seconds ahead of teammates Mike Conway, Kamui Kobayashi and José María López (who shared another Toyota GR010 Hybrid). It was Buemi's fourth Le Mans victory, Hartley's third, Hirakawa's first and Toyota's fifth in succession. A Glickenhaus SCG 007 LMH shared by Ryan Briscoe, Franck Mailleux and Richard Westbrook completed the podium, five laps behind in third place.


title: 2022 24 Hours of Le Mans

text: Jota's team of Roberto González, António Félix da Costa and Will Stevens, sharing an Oreca 07-Gibson car, won the Le Mans Prototype 2 (LMP2) category after leading for all but 15 laps. The debuting Prema squad of Lorenzo Colombo, Louis Delétraz and Robert Kubica followed, two minutes and 21 seconds later, and the class podium was completed by the sister Jota trio of Jonathan Aberdein, Ed Jones and Oliver Rasmussen in third place. In the final Le Mans Grand Touring Endurance Pro (LMGTE Pro) race at Le Mans, the No. 91 Porsche 911 RSR-19 of Gianmaria Bruni, Richard Lietz and Frédéric Makowiecki won the category; AF Corse's No. 51 Ferrari 488 GTE Evo, shared by James Calado, Alessandro Pier Guidi and Daniel Serra, was second. Aston Martin won the Le Mans Grand Touring Endurance Am (LMGTE AM) class with an TF Sport-run Aston Martin Vantage GTE, shared by Henrique Chaves, Ben Keating and Marco Sørensen, 44.446 seconds ahead of WeatherTech Racing's Porsche 911 RSR-19 driven by Julien Andlauer, Cooper MacNeil and Thomas Merrill.


title: 2022 24 Hours of Le Mans

text: The Alpine trio of André Negrão, Nicolas Lapierre and Matthieu Vaxivière remained atop the Hypercar Drivers' Championship; their advantage was reduced to three points over Buemi, Hartley and Hirakawa, who passed Glickenhaus' Romain Dumas and Olivier Pla for second. Bruni and Lietz took the GTE Drivers' Championship lead by three points over their Porsche teammates Michael Christensen and Kévin Estre. Toyota and Porsche left Le Mans as the respective Hypercar World Endurance and GTE Manufacturers' Championship leaders with three rounds remaining in the season.


title: 2022 24 Hours of Le Mans

text: The 24 Hours of Le Mans was first held in 1923 after automotive journalist Charles Faroux, Automobile Club de l'Ouest (ACO) general secretary Georges Durand and industrialist Emile Coquile agreed to conduct a test of vehicle reliability and durability. Considered one of the world's most prestigious motor races, it is part of the Triple Crown of Motorsport. The 2022 race, held at the Circuit de la Sarthe (near Le Mans, France) from 11 to 12 June 2022, was the event's 90th edition and the third round of the 2022 FIA World Endurance Championship. This was the first Le Mans race to host a full crowd and be run in June since restrictions were imposed in response to the COVID-19 pandemic in France.


title: 2022 24 Hours of Le Mans

text: Before the race, Alpine drivers André Negrão, Nicolas Lapierre and Matthieu Vaxivière led the Hypercar Drivers' Championship with 57 points. Glickenhaus' Romain Dumas and Olivier Pla were second with 39 points, and Toyota's Sébastien Buemi, Brendon Hartley and Ryō Hirakawa were third with 27. Porsche's Michael Christensen and Kévin Estre led the GTE Drivers' Championship with 57 points, ahead of AF Corse's James Calado and Alessandro Pier Guidi (43 points) and third-place Tommy Milner and Nick Tandy of Corvette (39 points). Alpine led Toyota in the Hypercar World Endurance Championship, and Porsche led Ferrari in the GTE Manufacturers' Championship.


title: 2022 24 Hours of Le Mans

text: Following the race, where clerk of the course Patrick Morrisseau was almost struck by an approaching car at the finish line, the ACO allowed Morrisseau to wave the checkered flag from a footbridge in the event of a close finish for safety reasons. For the first time in the event's history, all entries used Fédération Internationale de l'Automobile-compliant renewable fuel produced by TotalEnergies from wine residue to reduce carbon-dioxide emissions.


title: 2022 24 Hours of Le Mans

text: Entry to the race was initially open from 6 December 2021 to 28 February 2022. In response to the Russian G-Drive Racing team's suspension of its racing programme and measures imposed on Russian drivers and entries by international sporting bodies after the country's invasion of Ukraine, the ACO selection committee invited new applicants to apply for entry to the race from 7 to 9 March 2022. The committee issued 62 invitations, and entries were placed into the Le Mans Hypercar (LMH), Le Mans Prototype 2 (LMP2), Le Mans Grand Touring Endurance Professional (LMGTE Pro) and Le Mans Grand Touring Endurance Amateur (LMGTE Am) classes. Peugeot Sport withdrew their planned entries so they could continue testing their 9X8 Hypercars before homologation.


title: 2022 24 Hours of Le Mans

text: Teams which won their class in the 2021 24 Hours of Le Mans or won championships in the European Le Mans Series (ELMS), Asian Le Mans Series (ALMS) and the Michelin Le Mans Cup (MLMC), received automatic entry invitations. The second-place finishers in the 2021 ELMS in LMP2 and LMGTE championships also received an automatic invitation. Two participants from the IMSA SportsCar Championship (WTSC) were chosen by the ACO as automatic entries, regardless of performance or category. Teams earning automatic entries in LMP2 were allowed to change their cars from the previous year. ELMS LMGTE and ALMS GT teams earning automatic entries were allowed to use them in LMGTE Pro or LMGTE Am. The European and Asian LMP3 (Le Mans Prototype 3) champion was required to field an entry in LMP2, and the Michelin Le Mans Cup Group GT3 (GT3) champion was limited to the LMGTE Am category. The ACO announced the final list of automatic entries on 28 February 2022.


title: 2022 24 Hours of Le Mans

text: The ACO was scheduled to announce the 62-car list on 28 February but due to "administrative reasons", the announcement was delayed; it was published on 10 March. In addition to the 38 guaranteed WEC entries, 14 came from the ELMS, four each from IMSA and the ALMS, and three were one-off Le Mans entries. In addition to the 62 entries invited to the race, six (three each from LMP2 and LMGTE Am) were placed on a reserve list to replace withdrawn or unaccepted invitations. Reserve entries were ordered, with the first replacing the first withdrawal from the race regardless of class. Entries were selected for their sporting and technical quality, fan, media and public interest and commitment, and loyalty to other ACO-administered series.


title: 2022 24 Hours of Le Mans

text: After publication of the entry list, Racing Team Nederland withdrew its TDS Racing-run Oreca 07 entry from third in the reserve list to enable to team to focus on the IMSA endurance races. On 31 May, Hardpoint Motorsport (which received an automatic invitation through the IMSA for driver Rob Ferriol, who received the 2021 Akin Award as the highest-placed bronze-ranked IMSA entrant) withdrew their LMGTE Am-category Porsche 911 RSR-19 and relinquished the entry to Proton Competition. Proton gave it to the Absolute Racing customer squad, which raced under the Hardpoint Motorsport name in accordance with ACO regulations. Josh Pierson (driving the United Autosports Oreca 07-Gibson) was 16 years and 117 days old when he competed at Le Mans, beating the record set by Matt McMurry in 2014.


title: 2022 24 Hours of Le Mans

text: In the balance of performance adjustments, the Alpine A480-Gibson received a performance increase with an extra of power and weight; the Toyota GR010 Hybrid and the Glickenhaus SCG 007 LMH cars remained unchanged from the preceding 6 Hours of Spa-Francorchamps. The LMGTE Pro-class Chevrolet Corvette C8.R had its performance slowed by an engine-air-restrictor diameter reduction. The Ferrari 488 GTE Evo was equipped with a revised power curve it had since the WEC season began, and the Porsche 911 RSR-19 received a fuel-capacity increase in both LMGTE categories. Aston Martin's LMGTE Am-category Vantage AMR had its fuel capacity decreased by .


title: 2022 24 Hours of Le Mans

text: All entrants participated in eight hours of mandatory testing on 5 June, divided into two sessions. The testing took place in mainly-dry weather, with a brief period of light rain. Driver Paul di Resta helped Pierson in one of the United Autosports Oreca cars, while the team waited for Alex Lynn and Oliver Jarvis to arrive at Le Mans from Detroit.


title: 2022 24 Hours of Le Mans

text: The morning session was led by Toyota with a 3:31.626 lap from José María López's 7 entry with 17 minutes left, demoting Dumas' No. 708 Glickenhaus entry to second. Hartley made the No. 8 Toyota third-quickest, with Franck Mailleux's sister Glickenhaus No. 709 car fourth and the No. 36 Alpine of Vaxivière fifth. In LMP2, Jota's No. 38 car driven by Will Stevens lapped fastest at 3:33.964 during the third hour; United Autosport USA's No. 22 entry of Philip Hanson was second. The quickest Pro/Am sub-class entry was Mathias Beche's No. 13 TDS Racing car in third, and Alex Brundle's No. 34 Inter Europol Competition car was fourth in class. Corvette were first and second in LMGTE Pro, with Milner's No. 64 car faster than Nicky Catsburg's No. 63 sister entry by almost two-tenths of a second. The highest-placed Porsche was Gianmaria Bruni's No. 91 car in third, with the best Ferrari the privateer Riley Motorsports entry of Felipe Fraga placing fourth. Michelle Gatting's No. 85 Iron Dames Ferrari led in LMGTE Am ahead of the No. 52 AF Corse, LMGTE Pro's slowest entry. Some cars went off the track during the session, sustaining damage; it was stopped after ten minutes when the No. 65 Panis car of Julien Canal lost a wheel at the Daytona chicane on the Mulsanne Straight and was returned to the pit lane.


title: 2022 24 Hours of Le Mans

text: Dumas set the early pace in the second test session before López improved to a 3:29.986 lap with almost 90 minutes left to go. Hirakawa's No. 8 Toyota was third, and Mailleux was fourth in Glickenhaus' No. 709 car. Late in the session, López briefly went off the circuit during a car-safety procedure at Mulsanne Corner and forced the testing to end early. Filipe Albuquerque improved the fastest LMP2 lap to a 3:32.099 in the No. 22 United Autosports USA entry, and was fifth overall. The No. 38 Jota car of António Félix da Costa fell to second, and Lynn placed third in United Autosports' No. 23 sister vehicle. Alexander Sims improved the No. 64 Corvette's quickest lap to top LMGTE Pro, ahead of Davide Rigon's No. 51 AF Corse Ferrari and Frédéric Makowiecki's No. 91 Porsche. Ferrari were first and second in LMGTE Am, with Kessel Racing's No. 57 car of Mikkel Jensen leading JMW Motorsport's Renger van der Zande by four-tenths of a second. Safety cars were required for Charlie Fagg's stopped No. 777 D'Station Racing Aston Martin at the pit lane exit into turn one due to a sensor fault, and the No. 88 Dempsey Proton Porsche driven by Jan Heylen was beached in the gravel entering the Porsche Curves with punctured front tyres.


title: 2022 24 Hours of Le Mans

text: After testing, the ACO and FIA again altered the LMGTE balance of performance. The LMGTE Ferrari 488 GTE Evo received a decrease in turbocharger boost pressure curve across all revolutions, a fuel-capacity reduction from to , and minimum rear-wing angle changes to decrease performance. The Porsche 911 RSR-19 received a minimum rear-wing angle change to increase performance. The Pro-class Chevrolet Corvette C8.R and the Am-category Aston Martin Vantage AMR had no performance changes.


title: 2022 24 Hours of Le Mans

text: The first three-hour practice session was held on the afternoon of 8 June. Quick laps were initially disregarded as teams tried to conduct race simulations. Light rain had fallen on the circuit, and the session was declared wet before cars on slick tyres removed water. Hartley's No. 8 Toyota lapped fastest at 3:29.441 in the last 20 minutes, placing Mailleux's No. 709 Glickenhaus second. Glickenhaus' No. 708 sister entry of Pipo Derani was third, ahead of Kamui Kobayashi's No. 7 Toyota. Lynn's No. 23 United Autosports car was quickest in LMP2 and fourth overall at 3:30.238 in the session's final minutes. Félix da Costa put the No. 38 Jota car second just before practice ended, with Prema Orlen Team's No. 9 entry of Robert Kubica third. In LMGTE Pro, Corvette maintained its test-day pace with the No. 63 entry fastest after a lap by Antonio García demoted teammate Milner (in the No. 64 vehicle) to second. Porsche led in LMGTE Am, with the fastest class lap coming from the No. 79 WeatherTech Racing car driven by Julien Andlauer; brand mate Ben Barker's No. 86 GR Racing car was second. Several cars went off the track during the session. The full-course yellow procedure was deployed for Ryan Cullen's No. 10 Vector Sport car, which stopped in the Tertre Rouge S-curves. The session ended early when Steven Thomas damaged the No. 45 Algarve Pro Racing car's front left corner on the left tyre wall entering the Ford chicane.


title: 2022 24 Hours of Le Mans

text: Algarve Pro installed a new chassis on the No. 45 car, which missed qualifying. Dumas's No. 708 Glickenhaus car set the day's fastest time of 3:28.900 24 minutes into the second, two-hour evening session, 0.348 seconds faster than Kobayashi's second-place No. 7 Toyota. Toyota's No. 8 sister car was third after a lap by Hartley, and Ryan Briscoe's No. 709 Glickenhaus was fourth-quickest. René Rast recorded the quickest LMP2 lap at 3:33.119 in the No. 31 WRT vehicle, with Albuquerque's No. 22 United Autosports USA entry second. Dries Vanthoor was third with a late lap in Team WRT's No. 32 car. Fabio Scherer stopped the No. 43 Inter Europol car on the start-finish straight with right front suspension damage from mounting the sausage kerbs at the Ford chicane; a flatbed truck returned the car to the pit lane. Catsburg kept Corvette first in LMGTE Pro, as Makowiecki moved the No. 91 Porsche to second. LMGTE Am was led by Mikkel Pedersen's No. 46 Project 1 Racing Porsche with a lap set with five minutes remaining, leading Heylen's No. 88 Dempsey-Proton car.


title: 2022 24 Hours of Le Mans

text: Before the third practice session, a balance of performance adjustment gave the Alpine A480-Gibson more power and more energy per stint for a total power output of . The Toyota GR010 Hybrid and Glickenhaus SCG 007 LMH had no performance changes.


title: 2022 24 Hours of Le Mans

text: The third practice session, for three hours on the afternoon of 9 June, saw Kobayashi lap fastest early in the No. 7 Toyota; Hartley's No. 8 car was second. Both Glickenhaus cars were third and fourth, with Pla's No. 708 entry ahead of Briscoe's No. 709 sister car. Hirakawa stopped between the Indianapolis and Arnage corners with a hybrid problem, but slowly returned to the pit lane for a half-hour of repairs. LMP2 was led by Albuquerque's No. 22 United Autosports USA car, which was less than one-tenth of a second faster than teammate Lynn's No. 23 vehicle. They were followed by WRT's No. 31 car, driven by Robin Frijns. Tandy's No. 64 Corvette led LMGTE Pro, and Richard Lietz's No. 91 Porsche remained second in class. Pedersen kept the No. 46 Project 1 Porsche atop LMGTE Am, with the No. 33 TF Sport Aston Martin driven by Henrique Chaves slower by two-tenths of a second. Accidents by Philippe Cimadomo's No. 13 TDS Racing entry (against the right concrete barrier at the Porsche Curves from contact with Sean Gelael's No. 31 WRT car), the No. 39 Graff Racing car driven by Sebastien Page (spinning into the barrier exiting the Indianapolis turn) and Alexander West's No. 59 Inception Racing Ferrari (which struck the Ford Chicane tyre wall) disrupted the session.


title: 2022 24 Hours of Le Mans

text: The final two-hour practice session took place on the night of 9 June. Toyota led from the start with López's No. 7 entry going fastest overall at 3:28.322, 0.362 seconds quicker than Buemi's No. 8 sister car. The Glickenhaus team followed in third and fourth, with Derani's No. 708 entry faster than teammate Richard Westbrook's No. 708 car. Lynn's No. 23 United Autosport car led in LMP2 at 3:32.226, ahead of Panis Racing's Job van Uitert and Jonathan Aberdein's No. 28 Jota entry. Graff driver David Droux, in their No. 39 car, went across the gravel and crashed lightly against the tyre barrier at Mulsanne corner. Félix da Costa's No. 38 Jota car and Alexandre Cougnaud's No. 3 DKR Engineering entry collided at the Ford chicane, sending Cougnaud sideways into the tyre wall. Cougnaud drove across the circuit to the pit lane for repairs. Corvette continued their fast pace, with Catsburg lapping quickest in the No. 63 car in LMGTE Pro; the No. 64 sister C8R driven by Milner was second by 0.021 seconds. Dempsey-Proton led LMGTE Am with Harry Tincknell's No. 77 Porsche ahead of teammate Heylen in the second-place No. 88 entry.


title: 2022 24 Hours of Le Mans

text: Divided into two sessions, the first one-hour qualifying session set the race's starting order except for the fastest six vehicles in each class; they qualified for a half-hour shootout, "Le Mans Hyperpole", which determined pole position in all four classes. Cars were placed in starting order by category, with every Hypercar at the front of the field regardless of lap time, followed by LMP2, LMGTE Pro and LMGTE Am. The vehicles were placed with the six qualifying hyperpole cars ordered by fastest hyperpole-session lap time first, followed by the remaining non-qualifying class vehicles by fastest lap time set during the first qualifying session.


title: 2022 24 Hours of Le Mans

text: Each of the five entries in the Hypercar category progressed to hyperpole, with the fastest lap a 3:27.247 recorded by Kobayashi's No. 7 Toyota early before light rain fell during the second half of the session. In LMP2, the qualifiers were Frijns' No. 31 WRT car with entries from Jota's Félix da Costa, Norman Nato for RealTeam by WRT, the United Autosports pair of Lynn and Albuquerque and Prema's Louis Delétraz. LMGTE Pro saw the six factory entrants advance to hyperpole. The No. 92 Porsche driven by Laurens Vanthoor was fastest, ahead of García's No. 63 Corvette, Porsche's No. 91 car driven by Makowiecki, the No. 64 sister Corvette of Tandy and the AF Corse Ferrari entries driven by Calado (No. 51) and Antonio Fuoco (No. 52). LMGTE Am saw Nicki Thiim's No. 98 Northwest AMR, Jensen's Kessel Racing Ferrari, the No. 54 AF Corse Ferrari driven by Nick Cassidy, Rahel Frey's No. 85 Iron Dames Ferrari, Dempsey-Proton Racing's Tincknell in its No. 77 Porsche and the No. 61 AF Corse Ferrari driven by Vincent Abril. Actor Michael Fassbender lost control of the rear of Proton Competition's No. 93 Porsche braking for the first Mulsanne chicane due to a front puncture, and struck the Armco barrier with the front. Fassbender was unhurt, and the session was stopped for about 12 minutes to recover the damaged car. The crash resulted in the Proton Competition mechanics replacing the chassis on the No. 93 Porsche.


title: 2022 24 Hours of Le Mans

text: In hyperpole, Hartley set the fastest lap (3:24.408) in the No. 8 Toyota for Toyota's sixth consecutive pole position at Le Mans late in the session on worn tyres after being slowed by traffic in the Porsche Curves earlier on. Kobayashi qualified the No. 7 sister Toyota second after his fastest lap was deleted, reinstated and then invalidated again for a track-limits infringement at the Tertre Rouge corner. The No. 36 Alpine qualified third after a lap by Lapierre, and the Glickenhaus entries of Briscoe (No. 709) and Pla (No. 708) were fourth and fifth. The LMP2 pole position was taken by Frjins' No. 31 WRT entry, with a time of 3:28.394. Nato's No. 41 Realteam entry was second, holding the category pole until Frijns' lap. Following in third to sixth were the lead United Autosports car of Albuquerque, the Jota entry of Félix da Costa, Delétraz's Prema car and Lynn's sister United Autosports car (after one of Lynn's laps was invalidated). Corvette Racing took the first two positions in LMGTE Pro with Tandy's No. 63 entry on category pole, with the only sub-3:50 class lap from his teammate García's No. 64 car. The two Porsches were third and fourth, with Makowiecki's No. 91 car faster than Laurens Vanthoor's No. 92 vehicle. Abril took pole position in LMGTE Am in AF Corse's No. 61 Ferrari early in the session from Jensen's No. 57 Kessel entry and Tincknell's Dempsey-Proton Porsche after a lap by Frey in Iron Dames' No. 85 vehicle was invalidated for violating track limits.


title: 2022 24 Hours of Le Mans

text: After qualifying, stewards barred Cimadomo from racing at race director Eduardo Freitas's recommendation for his and other entrants' safety due to his "not driving to the standard required to safely participate in the remainder of the event" after his involvement in three incidents during free practice. Cimadomo was replaced by Formula E champion Nyck de Vries, and TDS' No. 13 car was moved from the LMP2 Pro/Am subclass to the main LMP2 category because De Vries held a platinum racing licence. The FIA and ACO revised the balance of performance, increasing the LMGTE Ferrari 488 GTE Evo's turbocharger boost pressure and decreasing the A480's engine power by and a loss of of energy allowance per stint.


title: 2022 24 Hours of Le Mans

text: A 15-minute warm-up session was held on the morning of 11 June, and a number of drivers did not have a fast lap due to incidents during the session. The No. 7 Toyota of Mike Conway lapped fastest at 3:31.236 seconds, ahead of the fastest LMP2 entry (driven by Rast) in WRT's No. 31 car; Buemi's No. 8 sister Toyota was 2.313 seconds slower in third, and second in Hypercar. The fastest LMGTE Pro lap was 3:54.788, set by Garcia in the No. 63 Corvette, and Toni Vilander's No. 21 AF Corse Ferrari paced LMGTE Am. Mailleux appeared to lose control of the No. 709 Glickenhaus leaving the Mulsanne turn due to a malfunctioning traction-control sensor before stopping on the right hand side of the circuit. A driveline fault slowed Tandy's No. 64 Corvette between the Mulsanne and Indianapolis corners, necessitating a pit stop. Nico Müller beaching the No. 10 Vector Sport car in the gravel at the Indianapolis corner and Laurents Hörr losing control of the No. 3 DKR entry at the Dunlop Chicane prompted a full-course-yellow period.


title: 2022 24 Hours of Le Mans

text: The weather was dry at the start, with an air temperature of and a track temperature of . There were 244,200 spectators in attendance. The French tricolour was waved at 16:00 CEST by TotalEnergies CEO Patrick Pouyanné to begin the race, which was led by the pole-sitting Buemi. Will Owen's No. 22 United Autosports USA Oreca, pinched between the WRT cars of Ferdinand Habsburg and LMP2-class pole-sitter Rast at the first corner, was sent into the gravel trap. Owen required recovery by crane to return to the pit lane for repairs (which cost him two laps), and Habsburg's No. 41 car sustained front-end damage and a right rear puncture. The stewards deemed Rast responsible for the accident, and imposed a one-minute stop-and-go penalty. This moved Kubica's No. 9 Prema entry on the inside from fifth to the LMP2 lead. In LMGTE Am, Abril was unable to retain the No. 61 AF Corse Ferrari's class lead; Tincknell used the end of a slow zone at turn one to overtake Jensen and Abril in Dempsey's No. 77 Porsche.


title: 2022 24 Hours of Le Mans

text: The race's first hour ended with Alessio Picariello's No. 99 Hardpoint Porsche taking the LMGTE Am lead from Project 1's No. 46 car, driven by Matteo Cairoli. Félix da Costa's No. 38 Jota entry became the new LMP2 leader after passing Prema's No. 9 Prema during the first pit-stop cycle. Buemi could not build up a large-enough lead over his teammate Conway due to an oversteer, and relinquished his overall lead to the No. 7 sister car after their pit stops; Conway's stop was faster. Tandy had trouble downshifting for the Mulsanne corner and drove across the roundabout to rejoin the circuit, but forfeited the No. 64 Corvette's hold on the LMGTE Pro lead to García's No. 63 sister Corvette. The LMGTE Am class became a battle between the No. 99 Hardpoint Ferrari and the No. 79 WeatherTech Racing Porsche, and Andlauer took the category lead by passing Picariello on the inside at the Indianapolis corner. Glickenhaus' No. 709 car, driven by Mailleux, was forced to the garage for three minutes for mechanics to replace a faulty engine sensor which was detected by telemetry just before the start of the third hour and fell to 10th place.


title: 2022 24 Hours of Le Mans

text: Dane Cameron and Felipe Nasr brought the No. 5 Team Penske Oreca car from ninth to second in LMP2 by the end of the third hour, ahead of Lorenzo Colombo's third-place No. 9 Prema car which drew to within a second of Nasr. Lapierre was observed speeding in a slow zone, and the No. 36 Alpine received a drive-through penalty which dropped the car from the lead lap. Team Project's No. 46 Porsche, driven by Nicolas Leutwiler, was beached in the Mulsanne Corner gravel and required extraction to get to the pit lane before the car was retired with irreparable ride height damage. The No. 7 Toyota lost the overall race lead to its No. 8 sister car when López went across the gravel at the second Mulsanne chicane on an out-lap. Vaxivière later brought the Alpine into the garage to repair an electronic clutch fault; the minutes of clutch bleeding dropped the car out of contention. Porsche began closing on the Corvette LMGTE Pro leaderswho were lapping faster in the cooler conditionsand overtook the No. 64 Corvette, which had downshifting problems after Tandy locked its brakes at the Mulsanne turn.


title: 2022 24 Hours of Le Mans

text: Sims brought the No. 64 Corvette back to second in LMGTE Pro, passing Laurens Vanthoor's No. 92 Porsche on the inside at the second Mulsanne chicane. In the sixth hour, Nasr's No. 5 Penske car lost its hold on second in LMP2 to Ricky Taylor's No. 37 Cool Racing vehicle when debris caused left-front-tyre delamination which damaged the car's left front corner. An unscheduled two-minute, 15-second pit stop dropped the car to third in LMP2 after brake-duct and front-end replacements. The No. 8 Toyota lost the overall lead to Kobayashi's No. 7 sister Toyota when Hirakawa was impeded by a GT car after exiting the pit lane. Corvette lost their hold on the top two places in LMGTE Pro when Tandy brought the No. 64 car into the garage for unscheduled brake repairs and García's No. 63 entry was forced slowly into the garage for a left rear suspension replacement. This promoted Christensen's No. 92 Porsche to the LMGTE Pro lead and Bruni's No. 91 sister car to second.