alibayram/wikipedia-40-langs huggingface dataset:
Yuen Chau Tsai

Yuen Chau Tsai was an island in Tolo Harbour, Hong Kong. It is now connected to land by a causeway after land reclamation. It is part of Tai Po New Town in the Tai Po District.

The Tai Wong Yeh Temple and Island House are located in the area of the former island.

Island House

Built in 1905, Island House was built as the residence for the first British Police Magistrate appointed in 1898. It is one of the declared monuments of Hong Kong.

Tai Wong Yeh Temple 
Tai Wong Yeh Temple () is located at the Island House Interchange. The temple was originally a stone tablet which was erected on the northern shore of Yuen Chau Tsai by the villagers in Chik Mei Village, located on the north bank of the Shenzhen River, in the mid-Qing Dynasty. In the late Qing Dynasty, some fishermen raised funds to build the temple for worship by local fishermen at the present location.

In 1960, a formal launching ceremony for dragon boats was first held at the Tai Wong Yeh Temple in Yuen Chau Tsai is held on Dragon Boat Festival. The ceremony has remained a tradition since then.

An opening ceremony was held in 1988 marking its renovation.

Yuen Chau Tsai (Island House) archaeological site
In 1960s, John Walden, who was the first one to report the site, collected stone adzes and geometric pottery sherds at the shoreline and the southern slope of Yuen Chau Tsai. In the 1980s and 1990s, field investigations recovered prehistoric cultural remains from the site.
.

References

Former islands of Hong Kong
Archaeological sites in Hong Kong
Tai Po District
Jammin' in New York

Jammin' in New York is George Carlin's 14th album and eighth HBO special, recorded on April 24 and 25, 1992, at the Paramount Theater, on the grounds of Madison Square Garden in New York City. Topics include the war in the Persian Gulf, similarities and differences among average Americans and language used at airports.

The album won a Grammy Award in 1993 for Best Spoken Comedy Album.

On-air HBO promos for the live broadcast on April 25, 1992, referred to the program as George Carlin: Live at the Paramount. Before the opening credits, the words "This show is for SAM" appear. This is a reference to comedian Sam Kinison, who had died in a car crash two weeks before the recording.

Carlin considered Jammin' in New York his favorite and best HBO special.

Track listing
"Rockets and Penises in the Persian Gulf" - 7:35
"Little Things We Share" - 7:47
"Airline Announcements" - 16:44
"Golf Courses for the Homeless" - 11:13
"The Planet Is Fine" - 13:37

References

1990s American television specials
1990s in comedy
HBO network specials
Stand-up comedy concert films
George Carlin live albums
Stand-up comedy albums
Spoken word albums by American artists
Live spoken word albums
1992 live albums
Grammy Award for Best Comedy Album
Albums recorded at Madison Square Garden
1992 television specials
1990s comedy albums
Vicia villosa

Vicia villosa, known as the hairy vetch, fodder vetch or winter vetch, is a plant native to some of Europe and western Asia. It is a legume, grown as a forage crop, fodder crop, cover crop, and green manure. Although non-native, it occurs in all US states and is considered invasive by some states, such as Alaska, Florida, Georgia, Kansas, Michigan, Minnesota, Oregon, and Washington state — as well as in Japan and some parts of Europe where it is not native. It is also found in most Canadian provinces.

Hairy vetch is very similar to tufted vetch (Vicia cracca), the most noticeable difference being that tufted vetch has a smooth stem.

Several subspecies are recognized:
 Vicia villosa ssp. ambigua (Guss.) Kerguelen (= ssp. elegantissima, ssp. pseudocracca)
 Vicia villosa ssp. eriocarpa (Hausskn.) P.W.Ball
 Vicia villosa ssp. microphylla (d'Urv.) P.W.Ball
 Vicia villosa ssp. varia (Host) Corb. (= ssp. dasycarpa)
 Vicia villosa ssp. villosa

The species Vicia hirsuta is also called hairy vetch.

Cultivation
Hairy vetch is widely used by organic growers in the United States as a winter cover crop and in no-till farming, as it is both winter hardy and can fix as much as 200 lb/acre of atmospheric nitrogen.  Disadvantages of hairy vetch in production agriculture are related to the crop having a portion of hard seed and its tendency to shatter seed early in the season, leading to it remaining in the field as a weed later in the season.  This can be a particular problem in wheat production.

Companion plant

Organic gardeners often plant hairy vetch (a nitrogen-fixing legume) as a companion plant to tomatoes, as an alternative to rotating crops in small growing areas.  When it is time to plant tomatoes in the spring, the hairy vetch is cut to the ground and the tomato seedlings are planted in holes dug through the matted residue and stubble. The vetch vegetation provides both nitrogen and an instant mulch that preserves moisture and keeps weeds from sprouting.

Alien or invasive species

It is regulated in the state of Florida. Some sources consider it generally invasive in areas with suitable climate for it to out-compete native species, in a manner similar to how cow vetch, Vicia cracca, is regarded. With both vetches, their agricultural usefulness is typically given precedence over concerns regarding potential ecological degradation. Despite being native to part of Europe it is considered an alien or invasive species in some European countries, such as Belgium, the Czech Republic, France, Germany, Italy, Poland, and Spain.

See also
Vicia spp. (vetch)
 List of companion plants

References

External links

Managing Cover Crops Profitably
Alternative Field Crops Manual
TurfFiles Hairy Vetch Weed ID
 Photo gallery

villosa
Flora of Europe
Flora of Western Asia
Nitrogen-fixing crops
Pentagrammic antiprism

In geometry, the pentagrammic antiprism is one in an infinite set of nonconvex antiprisms formed by triangle sides and two regular star polygon caps, in this case two pentagrams.

It has 12 faces, 20 edges and 10 vertices. This polyhedron is identified with the indexed name U79 as a uniform polyhedron.

Note that the pentagram face has an ambiguous interior because it is self-intersecting. The central pentagon region can be considered interior or exterior depending on how interior is defined. One definition of interior is the set of points that have a ray that crosses the boundary an odd number of times to escape the perimeter.

In either case, it is best to show the pentagram boundary line to distinguish it from a concave decagon.

Gallery

Net 
Net (fold the dotted line in the centre in the opposite direction to all the other lines):

See also
 Prismatic uniform polyhedron
Pentagrammic prism
Pentagrammic crossed-antiprism

References

External links 
 
http://www.mathconsult.ch/showroom/unipoly/04.html
https://web.archive.org/web/20050313233653/http://www.math.technion.ac.il/~rl/kaleido/data/04.html

Prismatoid polyhedra
Cueva del Fantasma

Cueva de El Fantasma (in Spanish, "Cave of The Phantom" after the comic book character) is a giant cave in southern Venezuela, located in one of the most biologically rich, geologically ancient parts of the world, along the slopes of Aprada-tepui. Large enough for two helicopters to land in the cave, the report from Zootaxa is said to be the first photographic evidence of such an immense cave. However, experts note, it is not technically a cave, but rather a collapsed, steep gorge.

References

External links
 Live Science

Caves of Venezuela
Pentagrammic crossed-antiprism

In geometry, the pentagrammic crossed-antiprism is one in an infinite set of nonconvex antiprisms formed by triangle sides and two regular star polygon caps, in this case two pentagrams.

It differs from the pentagrammic antiprism by having opposite orientations on the two pentagrams.

This polyhedron is identified with the indexed name U80 as a uniform polyhedron.

The pentagrammic crossed-antiprism may be inscribed within an icosahedron, and has ten triangular faces in common with the great icosahedron. It has the same vertex arrangement as the pentagonal antiprism. In fact, it may be considered as a parabidiminished great icosahedron.

See also
 Prismatic uniform polyhedron

External links 

http://www.mathconsult.ch/showroom/unipoly/80.html
 http://bulatov.org/polyhedra/uniform/u05.html
 https://web.archive.org/web/20050313234519/http://www.math.technion.ac.il/~rl/kaleido/data/05.html

Prismatoid polyhedra
Jesse Burr Strode

Jesse Burr Strode (February 18, 1845 – November 10, 1924) was an American Republican Party politician.

He was born in Fulton County, Illinois on February 18, 1845, and graduated from Abingdon College in Abingdon, Illinois (which was later consolidated with Eureka College). During the American Civil War he enlisted in Company G, Fiftieth Regiment, of the Illinois Volunteer Infantry serving from September 10, 1861, to the end of the war.

He returned to Abingdon first becoming principal of the schools from 1865 to 1873, being elected councilman six times and mayor twice. He moved to Plattsmouth, Nebraska and studied law passing the bar in and set up practice there in 1879. He was a district attorney from 1882 to 1888, moving to Lincoln, Nebraska in 1887. He was a district court judge in 1892. He was elected to the Fifty-fourth United States Congress and reelected to the Fifty-fifth United States Congress as a representative for the 1st district of Nebraska. He did not run for reelection in 1898, returning to Nebraska to become prosecuting attorney for the third district of Nebraska. He then became department commander of the Grand Army of the Republic in 1919 and 1920. He died in Lincoln on November 10, 1924, and is buried in Wyuka Cemetery.

References
 
 
 
 

1845 births
1924 deaths
People from Fulton County, Illinois
People of Illinois in the American Civil War
Illinois city council members
Mayors of places in Illinois
Nebraska state court judges
Republican Party members of the United States House of Representatives from Nebraska
People from Plattsmouth, Nebraska
Grand Army of the Republic officials
Strict father model

The strict father model of parenting is one which values strict discipline, particularly by the father, in parenting. The strict mother model also exists.

Ideas involved in this model include:
 That children learn through reward and punishment, as in operant conditioning. Corporal punishment, such as spanking, is favored in this model relative to other models. 
 That children become more self-reliant and more self-disciplined by having strict parents.
 That the parent, particularly the father, is meant to mete out rewards for good behavior as well as punish bad behavior.

This model of child-rearing would involve, for example, allowing children to cry themselves to sleep on the grounds that picking up a child when it should be sleeping on its own improperly fosters dependence on the parents. In his book Dare to Discipline, James Dobson advocates the strict father model.  However, some researchers have linked authoritarian childrearing with children who withdraw, lack spontaneity, and have lesser evidence of conscience.

The strict father model is discussed by George Lakoff in his books, including Moral Politics, Don't Think of an Elephant, The Political Mind, and Whose Freedom?. In these books, the strict father model is contrasted with the nurturant parent model. Lakoff argues that if the metaphor of nation as family and government as parent is used, then conservative politics correspond to the strict father model. For example, conservatives think that adults should refrain from looking to the government for assistance lest they become dependent.

References

External links
The Nation as Family. Rockridge Institute. Refer to chapter 4.
Two Worldviews - A History, Two Ideal Family Models and The Role of Empathy

Political science
Fatherhood
Parenting
Stellated truncated hexahedron

In geometry, the stellated truncated hexahedron (or quasitruncated hexahedron, and stellatruncated cube) is a uniform star polyhedron, indexed as U19. It has 14 faces (8 triangles and 6 octagrams), 36 edges, and 24 vertices. It is represented by Schläfli symbol t'{4,3} or t{4/3,3}, and Coxeter-Dynkin diagram, . It is sometimes called quasitruncated hexahedron because it is related to the truncated cube, , except that the square faces become inverted into {8/3} octagrams.

Even though the stellated truncated hexahedron is a stellation of the truncated hexahedron, its core is a regular octahedron.

Orthographic projections

Related polyhedra
It shares the vertex arrangement with three other uniform polyhedra: the convex rhombicuboctahedron, the small rhombihexahedron, and the small cubicuboctahedron.

See also
 List of uniform polyhedra

References

External links
 

Uniform polyhedra
Great cubicuboctahedron

In geometry, the great cubicuboctahedron is a nonconvex uniform polyhedron, indexed as U14. It has 20 faces (8 triangles, 6 squares and 6 octagrams), 48 edges, and 24 vertices. Its square faces and its octagrammic faces are parallel to those of a cube, while its triangular faces are parallel to those of an octahedron: hence the name cubicuboctahedron. The prefix great serves to distinguish it from the small cubicuboctahedron, which also has faces in the aforementioned directions.

Orthographic projections

Related polyhedra 

It shares the vertex arrangement with the convex truncated cube and two other nonconvex uniform polyhedra. It additionally shares its edge arrangement with the nonconvex great rhombicuboctahedron (having the triangular faces and 6 square faces in common), and with the great rhombihexahedron (having the octagrammic faces in common).

Great hexacronic icositetrahedron

The great hexacronic icositetrahedron (or great lanceal disdodecahedron) is the dual of the great cubicuboctahedron.

See also 
 List of uniform polyhedra

References

External links 
 
 

Polyhedra
Great icosidodecahedron

In geometry, the great icosidodecahedron is a nonconvex uniform polyhedron, indexed as U54. It has 32 faces (20 triangles and 12 pentagrams), 60 edges, and 30 vertices. It is given a Schläfli symbol r{3,}. It is the rectification of the great stellated dodecahedron and the great icosahedron. It was discovered independently by ,  and .

Related polyhedra 
The figure is a rectification of the great icosahedron or the great stellated dodecahedron, much as the (small) icosidodecahedron is related to the (small) icosahedron and (small) dodecahedron, and the cuboctahedron to the cube and octahedron.

It shares its vertex arrangement with the icosidodecahedron, which is its convex hull. Unlike the great icosahedron and great dodecahedron, the great icosidodecahedron is not a stellation of the icosidodecahedron, but a faceting of it instead.

It also shares its edge arrangement with the great icosihemidodecahedron (having the triangle faces in common), and with the great dodecahemidodecahedron (having the pentagram faces in common).

The truncated great stellated dodecahedron is a degenerate polyhedron, with 20 triangular faces from the truncated vertices, and 12 (hidden) pentagonal faces as truncations of the original pentagram faces, the latter forming a great dodecahedron inscribed within and sharing the edges of the icosahedron.

Great rhombic triacontahedron

The dual of the great icosidodecahedron is the great rhombic triacontahedron; it is nonconvex, isohedral and isotoxal.  It has 30 intersecting rhombic faces. It can also be called the great stellated triacontahedron.

The great rhombic triacontahedron can be constructed by expanding the size of the faces of a rhombic triacontahedron by a factor of τ3 = 1+2τ = 2+√5, where τ is the golden ratio.

See also 
 List of uniform polyhedra
 Rhombic hexecontahedron

Notes

References

External links 
 
 
 Uniform polyhedra and duals

Uniform polyhedra
Cubitruncated cuboctahedron

In geometry, the cubitruncated cuboctahedron or cuboctatruncated cuboctahedron is a nonconvex uniform polyhedron, indexed as U16. It has 20 faces (8 hexagons, 6 octagons, and 6 octagrams), 72 edges, and 48 vertices, and has a shäfli symbol of tr{4,3/2}

Convex hull 

Its convex hull is a nonuniform truncated cuboctahedron.

Orthogonal projection

Cartesian coordinates 
Cartesian coordinates for the vertices of a cubitruncated cuboctahedron are all the permutations of

 (±(−1), ±1, ±(+1))

Related polyhedra

Tetradyakis hexahedron

The tetradyakis hexahedron (or great disdyakis dodecahedron) is a nonconvex isohedral polyhedron. It has 48 intersecting scalene triangle faces, 72 edges, and 20 vertices.

Proportions 
The triangles have one angle of , one of  and one of . The dihedral angle equals . Part of each triangle lies within the solid, hence is invisible in solid models.

It is the dual of the uniform cubitruncated cuboctahedron.

See also 
 List of uniform polyhedra

References

 p. 92

External links 
 
 
 http://gratrix.net Uniform polyhedra and duals

Uniform polyhedra
West Lafayette Community School Corporation

West Lafayette Community School Corporation is a top rated, public school district located in West Lafayette, Indiana. It has 2,316 students in grades K-12 with a student-teacher ratio of 16 to 1. According to state test scores, 72% of students are at least proficient in math and 72% in reading.

The West Lafayette Community School Corporation administers the following schools in West Lafayette, Indiana, United States:
 West Lafayette Elementary School (Formerly known as Cumberland Elementary School)
 West Lafayette Intermediate School
 West Lafayette Junior-Senior High School
The superintendent is Shawn Greiner.

External links
 West Lafayette Community School Corporation

School districts in Indiana
West Lafayette, Indiana
Education in Tippecanoe County, Indiana
Truncated great dodecahedron

In geometry, the truncated great dodecahedron is a nonconvex uniform polyhedron, indexed as U37. It has 24 faces (12 pentagrams and 12 decagons), 90 edges, and 60 vertices. It is given a Schläfli symbol t{5,5/2}.

Related polyhedra 

It shares its vertex arrangement with three other uniform polyhedra: the nonconvex great rhombicosidodecahedron, the great dodecicosidodecahedron, and the great rhombidodecahedron; and with the uniform compounds of 6 or 12 pentagonal prisms.

This polyhedron is the truncation of the great dodecahedron:

The truncated small stellated dodecahedron looks like a dodecahedron on the surface, but it has 24 faces, 12 pentagons from the truncated vertices and 12 overlapping as (truncated pentagrams).

Small stellapentakis dodecahedron 

The small stellapentakis dodecahedron (or small astropentakis dodecahedron) is a nonconvex isohedral polyhedron. It is the dual of the truncated great dodecahedron. It has 60 intersecting triangular faces.

See also 
 List of uniform polyhedra

References

External links 
 
 
 Uniform polyhedra and duals

Nonconvex polyhedra
Uniform polyhedra
Small stellated truncated dodecahedron

In geometry, the small stellated truncated dodecahedron (or quasitruncated small stellated dodecahedron or small stellatruncated dodecahedron) is a nonconvex uniform polyhedron, indexed as U58. It has 24 faces (12 pentagons and 12 decagrams), 90 edges, and 60 vertices. It is given a Schläfli symbol t{,5}, and Coxeter diagram .

Related polyhedra 

It shares its vertex arrangement with three other uniform polyhedra: the convex rhombicosidodecahedron, the small dodecicosidodecahedron and the small rhombidodecahedron.

It also has the same vertex arrangement as the uniform compounds of 6 or 12 pentagrammic prisms.

See also 
 List of uniform polyhedra

References

External links 
 

Uniform polyhedra
Great stellated truncated dodecahedron

In geometry, the great stellated truncated dodecahedron (or quasitruncated great stellated dodecahedron or great stellatruncated dodecahedron) is a nonconvex uniform polyhedron, indexed as U66. It has 32 faces (20 triangles and 12 decagrams), 90 edges, and 60 vertices. It is given a Schläfli symbol t0,1{5/3,3}.

Related polyhedra 

It shares its vertex arrangement with three other uniform polyhedra: the small icosicosidodecahedron, the small ditrigonal dodecicosidodecahedron, and the small dodecicosahedron:

Cartesian coordinates 
Cartesian coordinates for the vertices of a great stellated truncated dodecahedron are all the even permutations of

 (0, ±τ, ±(2−1/τ))
 (±τ, ±1/τ, ±2/τ)
 (±1/τ2, ±1/τ, ±2)

where τ = (1+)/2 is the golden ratio (sometimes written φ).

See also 
 List of uniform polyhedra

References

External links 
 

Uniform polyhedra
Catherine of Foix, Countess of Candale

Catherine de Foix (c. 1455 – died before 1494) was a French noblewoman.

She was a daughter of Gaston IV, Count of Foix, and Eleanor of Navarre, and was a granddaughter of John II of Aragon and Blanche I of Navarre.

Catherine married Gaston de Foix, Count of Candale. They had:
Gaston de Foix, 3rd Count of Candale.
Jean de Foix, Archbishop of Bordeaux.
Pierre de Foix, died without issue.
Anne de Foix (1484-1506), married King Vladislaus II of Bohemia and Hungary.

References

Sources

1450s births
Year of birth uncertain
Year of death unknown
15th-century deaths
15th-century French people
15th-century French women
House of Foix
Navarrese infantas
Truncated great icosahedron

In geometry, the truncated great icosahedron (or great truncated icosahedron) is a nonconvex uniform polyhedron, indexed as U55. It has 32 faces (12 pentagrams and 20 hexagons), 90 edges, and 60 vertices. It is given a Schläfli symbol t{3,} or t0,1{3,} as a truncated great icosahedron.

Cartesian coordinates 
Cartesian coordinates for the vertices of a truncated great icosahedron centered at the origin are all the even permutations of

 (±1, 0, ±3/τ)
 (±2, ±1/τ, ±1/τ3)
 (±(1+1/τ2), ±1, ±2/τ)

where τ = (1+√5)/2 is the golden ratio (sometimes written φ). Using 1/τ2 = 1 − 1/τ one verifies that all vertices are on a sphere, centered at the origin, with the radius squared equal to 10−9/τ. The edges have length 2.

Related polyhedra 
This polyhedron is the truncation of the great icosahedron:

The truncated great stellated dodecahedron is a degenerate polyhedron, with 20 triangular faces from the truncated vertices, and 12 (hidden) pentagonal faces as truncations of the original pentagram faces, the latter forming a great dodecahedron inscribed within and sharing the edges of the icosahedron.

Great stellapentakis dodecahedron 

The great stellapentakis dodecahedron is a nonconvex isohedral polyhedron. It is the dual of the truncated great icosahedron. It has 60 intersecting triangular faces.

See also 
 List of uniform polyhedra

References

External links 
 
 
 Uniform polyhedra and duals

Uniform polyhedra
Great ditrigonal dodecicosidodecahedron

In geometry, the great ditrigonal dodecicosidodecahedron (or great dodekified icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U42. It has 44 faces (20 triangles, 12 pentagons, and 12 decagrams), 120 edges, and 60 vertices. Its vertex figure is an isosceles trapezoid.

Related polyhedra 

It shares its vertex arrangement with the truncated dodecahedron. It additionally shares its edge arrangement with the great icosicosidodecahedron (having the triangular and pentagonal faces in common) and the great dodecicosahedron (having the decagrammic faces in common).

See also 
 List of uniform polyhedra

References

External links 
 

Uniform polyhedra
Tony Award for Best Direction of a Musical

The Tony Award for Best Direction of a Musical has been given since 1960.  Before 1960 there was only one award for both play direction and musical direction, then in 1960 the award was split into two categories: Dramatic and Musical.

Winners and nominees
† indicates the winner for the annual Tony Award for Best Musical

* indicates the winner for the annual Tony Award for Best Revival of a Musical

1950s

1960s

1970s

1980s

1990s

2000s

2010s

2020s

Multiple wins

8 Wins
 Harold Prince

3 Wins
 Gower Champion
 Tommy Tune

2 Wins
 George Abbott
 Michael Bennett
 Wilford Leach
 Des McAnuff
 Trevor Nunn
 Jerome Robbins

Multiple nominations

16 Nominations
 Harold Prince

8 Nominations
 Gower Champion

7 Nominations
 Scott Ellis

6 Nominations
 Bob Fosse
 James Lapine
 Casey Nicholaw
 Trevor Nunn
 Tommy Tune

5 Nominations
 Michael Bennett
 Des McAnuff
 Jack O'Brien
 Jerry Zaks

4 Nominations
 Michael Greif
 Richard Maltby Jr.
 Kathleen Marshall
 Michael Mayer
 Diane Paulus
 Bartlett Sher
 Susan Stroman
 George C. Wolfe

3 Nominations
 George Abbott
 Michael Arden
 Christopher Ashley
 Michael Blakemore
 John Doyle
 Michael Kidd
 Arthur Laurents
 Robert Moore
 Jerome Robbins
 Gene Saks
 Burt Shevelove

2 Nominations
 Vinnette Carroll
 Martin Charnin
 Rachel Chavkin
 Cy Feuer
 Nicholas Hytner
 Thomas Kail
 Joe Layton
 Wilford Leach
 Joshua Logan
 Mike Nichols
 Mike Ockrent
 Hector Orezzoli
 John Rando
 Claudio Segovia
 Julie Taymor
 Matthew Warchus
 Christopher Wheeldon

Female winners and nominees
Out of 22 women nominated for 34 musicals, only 5 women have won this award for 5 musicals:

Bold represents winner

See also
 Tony Award for Best Direction of a Play
 Drama Desk Award for Outstanding Director of a Musical
 Laurence Olivier Award for Best Director
 List of Tony Award-nominated productions

References

External links
 Tony Awards Official site
 Tony Award for Direction of a Musical, Internet Broadway Database
 Tony Awards at broadwayworld.com

Tony Awards
Awards established in 1950
1950 establishments in the United States
Taluks of Bangalore Urban district

The Indian city of Bengaluru has four taluks in Bangalore Urban district in Karnataka:

Hebbala(Bengaluru North)
Yelahanka
Kengeri(Bengaluru South)
Krishnarajapura(Bengaluru East)
Anekal

References

Geography of Bangalore
Taluks of Karnataka
Great dodecicosidodecahedron

In geometry, the great dodecicosidodecahedron (or great dodekicosidodecahedron) is a nonconvex uniform polyhedron, indexed as U61. It has 44 faces (20 triangles, 12 pentagrams and 12 decagrams), 120 edges and 60 vertices.

Related polyhedra 

It shares its vertex arrangement with the truncated great dodecahedron and the uniform compounds of 6 or 12 pentagonal prisms. It additionally shares its edge arrangement with the nonconvex great rhombicosidodecahedron (having the triangular and pentagrammic faces in common), and with the great rhombidodecahedron (having the decagrammic faces in common).

See also 
 List of uniform polyhedra

References

External links 
 

Uniform polyhedra
Small icosicosidodecahedron

In geometry, the small icosicosidodecahedron (or small icosified icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U31. It has 52 faces (20 triangles, 12 pentagrams, and 20 hexagons), 120 edges, and 60 vertices.

Related polyhedra 

It shares its vertex arrangement with the great stellated truncated dodecahedron. It additionally shares its edges with the small ditrigonal dodecicosidodecahedron (having the triangular and pentagrammic faces in common) and the small dodecicosahedron (having the hexagonal faces in common).

See also 
 List of uniform polyhedra

References

External links 
 

Uniform polyhedra
Rhombidodecadodecahedron

In geometry, the rhombidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U38. It has 54 faces (30 squares, 12 pentagons and 12 pentagrams), 120 edges and 60 vertices. It is given a Schläfli symbol t0,2, and by the Wythoff construction this polyhedron can also be named a cantellated great dodecahedron.

Cartesian coordinates 
Cartesian coordinates for the vertices of a uniform great rhombicosidodecahedron are all the even permutations of

 (±1/τ2, 0, ±τ2)
 (±1, ±1, ±)
 (±2, ±1/τ, ±τ)

where τ = (1+)/2 is the golden ratio (sometimes written φ).

Related polyhedra 

It shares its vertex arrangement with the uniform compounds of 10 or 20 triangular prisms. It additionally shares its edges with the icosidodecadodecahedron (having the pentagonal and pentagrammic faces in common) and the rhombicosahedron (having the square faces in common).

Medial deltoidal hexecontahedron

The medial deltoidal hexecontahedron (or midly lanceal ditriacontahedron) is a nonconvex isohedral polyhedron. It is the dual of the rhombidodecadodecahedron. It has 60 intersecting quadrilateral faces.

See also 
 List of uniform polyhedra

References

External links 
 
 
 Uniform polyhedra and duals

Uniform polyhedra
Doddabettahalli

Doddabettahalli is a village located in the Bangalore North Taluk, Karnataka, India. It is the highest natural point in Bangalore. The gentle slopes and valleys on either side of this ridge hold better prospects of ground water utilization. The low-lying areas are marked by a series of tanks varying in size from a small pond to those of considerable extent, but all very shallow.

See also 

 Bangalore Urban District
 Districts of Karnataka

References 

Villages in Bangalore Rural district

External links 
 https://bengaluruurban.nic.in/en/
Icositruncated dodecadodecahedron

In geometry, the icositruncated dodecadodecahedron or icosidodecatruncated icosidodecahedron is a nonconvex uniform polyhedron, indexed as U45.

Convex hull 

Its convex hull is a nonuniform truncated icosidodecahedron.

Cartesian coordinates 
Cartesian coordinates for the vertices of an icositruncated dodecadodecahedron are all the even permutations of

 (±(2−1/τ), ±1, ±(2+τ))
 (±1, ±1/τ2, ±(3τ−1))
 (±2, ±2/τ, ±2τ)
 (±3, ±1/τ2, ±τ2)
 (±τ2, ±1, ±(3τ−2))

where τ = (1+)/2 is the golden ratio (sometimes written φ).

Related polyhedra

Tridyakis icosahedron

The tridyakis icosahedron is the dual polyhedron of the icositruncated dodecadodecahedron. It has 44 vertices, 180 edges, and 120 scalene triangular faces.

See also
 Catalan solid Duals to convex uniform polyhedra
 Uniform polyhedra
 List of uniform polyhedra

References
 Photo on page 96, Dorman Luke construction and stellation pattern on page 97.

External links 
 

Uniform polyhedra
Truncated dodecadodecahedron

In geometry, the truncated dodecadodecahedron (or stellatruncated dodecadodecahedron) is a nonconvex uniform polyhedron, indexed as U59. It is given a Schläfli symbol t0,1,2{,5}. It has 54 faces (30 squares, 12 decagons, and 12 decagrams), 180 edges, and 120 vertices. The central region of the polyhedron is connected to the exterior via 20 small triangular holes.

The name truncated dodecadodecahedron is somewhat misleading: truncation of the  dodecadodecahedron would produce rectangular faces rather than squares, and the pentagram faces of the dodecadodecahedron would turn into truncated pentagrams rather than decagrams. However, it is the quasitruncation of the dodecadodecahedron, as defined by . For this reason, it is also known as the quasitruncated dodecadodecahedron. Coxeter et al. credit its discovery to a paper published in 1881 by Austrian mathematician Johann Pitsch.

Cartesian coordinates 
Cartesian coordinates for the vertices of a truncated dodecadodecahedron are all the triples of numbers obtained by circular shifts and sign changes from the following points (where  is the golden ratio):

Each of these five points has eight possible sign patterns and three possible circular shifts, giving a total of 120 different points.

As a Cayley graph
The truncated dodecadodecahedron forms a Cayley graph for the symmetric group on five elements, as generated by two group members: one that swaps the first two elements of a five-tuple, and one that performs a circular shift operation on the last four elements. That is, the 120 vertices of the polyhedron may be placed in one-to-one correspondence with the 5! permutations on five elements, in such a way that the three neighbors of each vertex are the three permutations formed from it by swapping the first two elements or circularly shifting (in either direction) the last four elements.

Related polyhedra

Medial disdyakis triacontahedron

The medial disdyakis triacontahedron is a nonconvex isohedral polyhedron. It is the dual of the uniform truncated dodecadodecahedron.

See also 
 List of uniform polyhedra

References

External links 
 
 

Uniform polyhedra
Great truncated icosidodecahedron

In geometry, the great truncated icosidodecahedron (or great quasitruncated icosidodecahedron or stellatruncated icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U68. It has 62 faces (30 squares, 20 hexagons, and 12 decagrams), 180 edges, and 120 vertices. It is given a Schläfli symbol t0,1,2, and Coxeter-Dynkin diagram, .

Cartesian coordinates 
Cartesian coordinates for the vertices of a great truncated icosidodecahedron centered at the origin are all the even permutations of
 (±τ, ±τ, ±(3−1/τ)),
 (±2τ, ±1/τ, ±τ−3),
 (±τ, ±1/τ2, ±(1+3/τ)),
 (±, ±2, ±/τ) and
 (±1/τ, ±3, ±2/τ),
where τ = (1+)/2 is the golden ratio.

Related polyhedra

Great disdyakis triacontahedron 

The great disdyakis triacontahedron (or trisdyakis icosahedron) is a nonconvex isohedral polyhedron. It is the dual of the great truncated icosidodecahedron. Its faces are triangles.

Proportions 
The triangles have one angle of , one of  and one of . The dihedral angle equals . Part of each triangle lies within the solid, hence is invisible in solid models.

See also 
 List of uniform polyhedra

References

 p. 96

External links 
 
 

Uniform polyhedra
Asclettin, Count of Aversa

Asclettin Drengot (also Ascletin or Asclettino) was the son of Asclettin, count of Acerenza, brother of Rainulf Drengot, whom he succeeded in the county of Aversa in 1045. He was duly elected by the Norman nobles of Aversa and invested with the countship by his suzerain, Guaimar IV of Salerno. 

Asclettin did not immediately come into possession of the duchy of Gaeta, which Ranulf had ruled as a vassal of Guaimar. Instead, the Gaetans chose Atenulf, Count of Aquino, as duke. Guaimar attacked and defeated him on behalf of Asclettin, but in return for his assistance against Pandulf the Wolf, then assaulting Monte Cassino, he freed him and confirmed in Gaeta. 

Asclettin only ruled a few months before dying prematurely. He was succeeded by his cousin Rainulf Trincanocte. His younger brother Richard later succeeded to Aversa and brought the family the principality of Capua as well.

|-

1045 deaths
Italo-Normans
Norman warriors
Counts of Aversa
Dukes of Gaeta
Year of birth unknown
Great snub icosidodecahedron

In geometry, the great snub icosidodecahedron is a nonconvex uniform polyhedron, indexed as U57. It has 92 faces (80 triangles and 12 pentagrams), 150 edges, and 60 vertices. It can be represented by a Schläfli symbol sr{,3}, and Coxeter-Dynkin diagram .

This polyhedron is the snub member of a family that includes the great icosahedron, the great stellated dodecahedron and the great icosidodecahedron.

In the book Polyhedron Models by Magnus Wenninger, the polyhedron is misnamed great inverted snub icosidodecahedron, and vice versa.

Cartesian coordinates 
Cartesian coordinates for the vertices of a great snub icosidodecahedron are all the even permutations of
 (±2α, ±2, ±2β),
 (±(α−βτ−1/τ), ±(α/τ+β−τ), ±(−ατ−β/τ−1)),
 (±(ατ−β/τ+1), ±(−α−βτ+1/τ), ±(−α/τ+β+τ)),
 (±(ατ−β/τ−1), ±(α+βτ+1/τ), ±(−α/τ+β−τ)) and
 (±(α−βτ+1/τ), ±(−α/τ−β−τ), ±(−ατ−β/τ+1)),
with an even number of plus signs, where
 α = ξ−1/ξ
and
 β = −ξ/τ+1/τ2−1/(ξτ),
where τ = (1+)/2 is the golden mean and
ξ is the negative real root of ξ3−2ξ=−1/τ, or approximately −1.5488772.
Taking the odd permutations of the above coordinates with an odd number of plus signs gives another form, the enantiomorph of the other one.

The circumradius for unit edge length is

where  is the second largest real root of the polynomial .

The four positive real roots of the sextic in 

are, in order, the circumradii of the great retrosnub icosidodecahedron (U74), great snub icosidodecahedron (U57), great inverted snub icosidodecahedron (U69) and snub dodecahedron (U29).

Related polyhedra

Great pentagonal hexecontahedron 

The great pentagonal hexecontahedron (or great petaloid ditriacontahedron) is a nonconvex isohedral polyhedron and dual to the uniform great snub icosidodecahedron. It has 60 intersecting irregular pentagonal faces, 120 edges, and 92 vertices.

Proportions

Denote the golden ratio by . Let  be the negative zero of the polynomial . Then each pentagonal face has four equal angles of  and one angle of . Each face has three long and two short edges. The ratio  between the lengths of the long and the short edges is given by
. 
The dihedral angle equals . Part of each face lies inside the solid, hence is invisible in solid models. The other two zeroes of the polynomial  play a similar role in the description of the great inverted pentagonal hexecontahedron and the great pentagrammic hexecontahedron.

See also 
 List of uniform polyhedra
 Great inverted snub icosidodecahedron
 Great retrosnub icosidodecahedron

References

External links 
 
 

Uniform polyhedra
Karavas

Karavas (;  is a town in the north of the Cyprus island. It is under the de facto control of Northern Cyprus. , the town has a population of 6,597.

Etymology
The name Karavas comes from the Greek karávi (), meaning "ship".
The name Alsancak comes from the two turkish words Al, meaning "Red" and 'Sancak meaning "flag".

History

Prior to the Turkish invasion in 1974, Karavas had a Greek population of approximately 2200. Karavas was captured by the Turkish Army before the second Turkish invasion of Cyprus after July 20, 1974. The city was attacked on August 6, during the so-called armistice. All Greek Cypriot inhabitants were forced out of Karavas by Turkish military forces and have become refugees, living in Cyprus and abroad. Following the population exchange assisted by the United Nations where the Turkish Cypriots forced from their villages in the South were transported to the safety of the North, today the village is home mostly to those Turkish Cypriots displaced from their original village Mandria in the Paphos region left in the south of the island.

The Turkish Cypriot municipality Alsancak was founded in 1974.

"Pente Mili" is one of the most beautiful beaches in Karavas.

The Cyprus Treasure, an impressive collection of silver vessels, dishes, spoons and jewelry, was found here in 1902 and 1917. It can be found in the British Museum in London, Metropolitan Museum of Art in New York City and the Cyprus Museum in Nicosia.

Notable people
Karavas is the birthplace of the Cypriot-American organic chemist K. C. Nicolaou.

International relations

Twin towns – sister cities
Karavas is twinned with:
 Bornova, İzmir, Turkey (since 2011)
 Gazipaşa, Antalya, Turkey (since 2015)

References 

Municipalities in Kyrenia District
Populated places in Girne District
Municipalities of Northern Cyprus
Small snub icosicosidodecahedron

In geometry, the small snub icosicosidodecahedron or snub disicosidodecahedron is a uniform star polyhedron, indexed as U32. It has 112 faces (100 triangles and 12 pentagrams), 180 edges, and 60 vertices. Its stellation core is a truncated pentakis dodecahedron. It also called a holosnub icosahedron, ß{3,5}.

The 40 non-snub triangular faces form 20 coplanar pairs, forming star hexagons that are not quite regular. Unlike most snub polyhedra, it has reflection symmetries.

Convex hull 

Its convex hull is a nonuniform truncated icosahedron.

Cartesian coordinates 
Cartesian coordinates for the vertices of a small snub icosicosidodecahedron are all the even permutations of

 (±(1-ϕ+α), 0, ±(3+ϕα))
 (±(ϕ-1+α), ±2, ±(2ϕ-1+ϕα))
 (±(ϕ+1+α), ±2(ϕ-1), ±(1+ϕα))

where ϕ = (1+)/2 is the golden ratio and α = .

See also 
 List of uniform polyhedra
 Small retrosnub icosicosidodecahedron

External links 
 
 

Uniform polyhedra
Snub dodecadodecahedron

In geometry, the snub dodecadodecahedron is a nonconvex uniform polyhedron, indexed as . It has 84 faces (60 triangles, 12 pentagons, and 12 pentagrams), 150 edges, and 60 vertices. It is given a Schläfli symbol  as a snub great dodecahedron.

Cartesian coordinates 
Cartesian coordinates for the vertices of a snub dodecadodecahedron are all the even permutations of
 (±2α, ±2, ±2β),
 (±(α+β/τ+τ), ±(-ατ+β+1/τ), ±(α/τ+βτ-1)),
 (±(-α/τ+βτ+1), ±(-α+β/τ-τ), ±(ατ+β-1/τ)),
 (±(-α/τ+βτ-1), ±(α-β/τ-τ), ±(ατ+β+1/τ)) and
 (±(α+β/τ-τ), ±(ατ-β+1/τ), ±(α/τ+βτ+1)),
with an even number of plus signs, where
 β = (α2/τ+τ)/(ατ−1/τ),
where τ = (1+)/2 is the golden mean and
α is the positive real root of τα4−α3+2α2−α−1/τ, or approximately 0.7964421.
Taking the odd permutations of the above coordinates with an odd number of plus signs gives another form, the enantiomorph of the other one.

Related polyhedra

Medial pentagonal hexecontahedron 

The medial pentagonal hexecontahedron is a nonconvex isohedral polyhedron. It is the dual of the snub dodecadodecahedron. It has 60 intersecting irregular pentagonal faces.

See also 
 List of uniform polyhedra
 Inverted snub dodecadodecahedron

References

External links 
 
 

Uniform polyhedra
Tony Award for Best Orchestrations

The Tony Award for Best Orchestrations is awarded to acknowledge the contributions of musical orchestrators in both musicals and plays. The award has been given since 1997.

Winners and nominees

1990s

2000s

2010s

2020s

Multiple wins

3 Wins
 Doug Besterman
 Alex Lacamoire

2 Wins
 Ralph Burns
 Stephen Oremus
 Charlie Rosen
 Don Sebesky
 Michael Starobin

Multiple nominations

11 Nominations
 Jonathan Tunick

9 Nominations
 Larry Hochman

7 Nominations
 Harold Wheeler

5 Nominations
 Doug Besterman

4 Nominations
 Bill Brohn
 John Clancy
 Don Sebesky
 Danny Troob

3 Nominations
 Larry Blank
 Bruce Coughlin
 Bill Elliott
 Tom Kitt
 Alex Lacamoire
 Charlie Rosen
 Michael Starobin
 Daryl Waters

2 Nominations
 Ralph Burns
 Jason Carr
 David Cullen
 Simon Hale
 Michael Gibson
 Martin Koch
 Stephen Oremus
 Bill Sherman

See also
 Tony Award for Best Original Score
 Drama Desk Award for Outstanding Orchestrations
 Laurence Olivier Award for Best Original Score or New Orchestrations
 List of Tony Award-nominated productions

External links
Tony Awards Official site
Tony Awards at Internet Broadway database Listing
Tony Awards at broadwayworld.com

References

 
Tony Awards
Awards established in 1997
1997 establishments in the United States
Ditrigonal dodecadodecahedron

In geometry, the ditrigonal dodecadodecahedron (or ditrigonary dodecadodecahedron) is a nonconvex uniform polyhedron, indexed as U41. It has 24 faces (12 pentagons and 12 pentagrams), 60 edges, and 20 vertices. It has extended Schläfli symbol b{5,}, as a blended great dodecahedron, and Coxeter diagram . It has 4 Schwarz triangle equivalent constructions, for example Wythoff symbol 3 |  5, and Coxeter diagram .

Related polyhedra 

Its convex hull is a regular dodecahedron. It additionally shares its edge arrangement with the small ditrigonal icosidodecahedron (having the pentagrammic faces in common), the great ditrigonal icosidodecahedron (having the pentagonal faces in common), and the regular compound of five cubes.

Furthermore, it may be viewed as a facetted dodecahedron: the pentagrammic faces are inscribed in the dodecahedron's pentagons. Its dual, the medial triambic icosahedron, is a stellation of the icosahedron.

It is topologically equivalent to a quotient space of the hyperbolic order-6 pentagonal tiling, by distorting the pentagrams back into regular pentagons. As such, it is a regular polyhedron of index two:

See also 
 List of uniform polyhedra

References

External links 
 

Uniform polyhedra
Great dodecahemidodecahedron

In geometry, the great dodecahemidodecahedron is a nonconvex uniform polyhedron, indexed as U70. It has 18 faces (12 pentagrams and 6 decagrams), 60 edges, and 30 vertices. Its vertex figure is a crossed quadrilateral.

Aside from the regular small stellated dodecahedron {5/2,5} and great stellated dodecahedron {5/2,3}, it is the only nonconvex uniform polyhedron whose faces are all non-convex regular polygons (star polygons), namely the star polygons {5/2} and {10/3}.

It is a hemipolyhedron with 6 decagrammic faces passing through the model center.

Related polyhedra 

Its convex hull is the icosidodecahedron. It also shares its edge arrangement with the great icosidodecahedron (having the pentagrammic faces in common) and the great icosihemidodecahedron (having the decagrammic faces in common).

Gallery

See also 
 List of uniform polyhedra

References

External links 
 
 Uniform polyhedra and duals

Uniform polyhedra
Small dodecahemicosahedron

In geometry, the small dodecahemicosahedron (or great dodecahemiicosahedron) is a nonconvex uniform polyhedron, indexed as U62. It has 22 faces (12 pentagrams and 10 hexagons), 60 edges, and 30 vertices. Its vertex figure is a crossed quadrilateral.

It is a hemipolyhedron with ten hexagonal faces passing through the model center.

Related polyhedra 

Its convex hull is the icosidodecahedron. It also shares its edge arrangement with the dodecadodecahedron (having the pentagrammic faces in common), and with the great dodecahemicosahedron (having the hexagonal faces in common).

Gallery

See also 
 List of uniform polyhedra

References

External links 
 
 Uniform polyhedra and duals

Uniform polyhedra
Great dodecahemicosahedron

In geometry, the great dodecahemicosahedron (or great dodecahemiicosahedron) is a nonconvex uniform polyhedron, indexed as U65. It has 22 faces (12 pentagons and 10 hexagons), 60 edges, and 30 vertices. Its vertex figure is a crossed quadrilateral.

It is a hemipolyhedron with ten hexagonal faces passing through the model center.

Related polyhedra 

Its convex hull is the icosidodecahedron. It also shares its edge arrangement with the dodecadodecahedron (having the pentagonal faces in common), and with the small dodecahemicosahedron (having the hexagonal faces in common).

Great dodecahemicosacron 

The great dodecahemicosacron is the dual of the great dodecahemicosahedron, and is one of nine dual hemipolyhedra. It appears visually indistinct from the small dodecahemicosacron.

Since the hemipolyhedra have faces passing through the center, the dual figures have corresponding vertices at infinity; properly, on the real projective plane at infinity. In Magnus Wenninger's Dual Models, they are represented with intersecting prisms, each extending in both directions to the same vertex at infinity, in order to maintain symmetry. In practice, the model prisms are cut off at a certain point that is convenient for the maker. Wenninger suggested these figures are members of a new class of stellation figures, called stellation to infinity. However, he also suggested that strictly speaking, they are not polyhedra because their construction does not conform to the usual definitions.

The great dodecahemicosahedron can be seen as having ten vertices at infinity.

See also 
 List of uniform polyhedra
 Hemi-icosahedron - The ten vertices at infinity correspond directionally to the 10 vertices of this abstract polyhedron.

References

 (Page 101, Duals of the (nine) hemipolyhedra)

External links 
 
 
 Uniform polyhedra and duals

Uniform polyhedra
Phari

Phari or Pagri (; ) is a town in Yadong County in the Tibet Autonomous Region, China near the border with Bhutan. The border can be accessed through a secret road/trail connecting Tsento Gewog in Bhutan () known as Tremo La.  the town had a population of 2,121. It is one of the highest towns in the world, being about  above sea-level at the head of the Chumbi Valley.

History
Thomas Manning, the first Englishman to reach Lhasa, visited Pagri from 21September until 5November 1811 and had this to say about his room in the town: "Dirt, dirt, grease, smoke. Misery, but good mutton." The Pagri Fortress (Dzong) was located here and was important for the government as it stood between Tibet and Bhutan. Pagri was a staging area en route to Gyantse and ultimately Lhasa.

Thubten Ngodup, the current Nechung Oracle, was born in Phari in 1957.

Gallery

Climate 
Owing to its extreme altitude, Pagri has an alpine climate (Köppen ETH) that is too cold to permit the growth of trees, even though the altitude is still marginally too low for the formation of permafrost. Example Mount Fuji in Japan, Uelen in Russia and Longyearbyen in Svalbard Norway. The winter is severe in spite of the fact that no month has daytime maxima below , and also very dry and long, extending as late as May. Snowfall, however, is rare because of the dryness. Summers, during which the great majority of precipitation occurs, are cool even at their warmest and consistently damp, even though the Himalayas prevent falls from ever being heavy.

References

Populated places in Shigatse
Bhutan–China border crossings
Township-level divisions of Tibet
Yadong County