# List of hyperboloid structures

This page is a list of hyperboloid structures. These were first applied in architecture by Russian engineer Vladimir Shukhov (1853–1939). Shukhov built his first example as a water tower (hyperbolic shell) for the 1896 All-Russian Exposition. Subsequently, more have been designed by other architects, including Le Corbusier, Antoni Gaudí, Eduardo Torroja, Oscar Niemeyer and Ieoh Ming Pei.
The shapes are doubly ruled surfaces, which can be classed as:
* Hyperbolic paraboloids, such as saddle roofs
* Hyperboloid of one sheet, such as cooling towers
* A hyperboloid of one sheet is a doubly ruled surface, and it may be generated by either of two families of straight lines.
* The hyperbolic paraboloid is a doubly ruled surface so it may be used to construct a saddle roof from straight beams.

## Notable projects

| Structure | Date completed | Location | Country | Function | Height | Architect | Notes |
| Shukhov Tower in Polibino | 1896 | Polibino | Russia | Hyperboloid water tower | 37 m (121 ft) | Vladimir Shukhov | The world's first hyperboloid structure featured at the 1896 All-Russian Exposition in Nizhny Novgorod, Russia. |
| Adziogol Lighthouse | 1911 | Kherson | Ukraine | Hyperboloid lighthouse tower | 64 m (211 ft) | Vladimir Shukhov | Illustrates a hyperboloid lattice. |
| Stanislav Range Front Light | 1911 | Kherson | Ukraine | Hyperboloid lighthouse tower | 26 m (85 ft) | Vladimir Shukhov | |
| Church of Colònia Güell | 1915 | Santa Coloma de Cervelló | Spain | Hyperboloid building cathedral vaults | | Antoni Gaudí | An unfinished building with hyperbolic paraboloid vaults. |
| Shukhov Tower | 1922 | Moscow | Russia | Hyperboloid broadcast tower | 160 m (525 ft) | Vladimir Shukhov | Unless the international campaign can save it, the 1922 Shukhov Tower is under current threat of demolition. |
| Shukhov tower on the Oka River | 1929 | Nizhny Novgorod | Russia | Hyperboloid electricity pylon towers | 128 m (420 ft) | Vladimir Shukhov | The Shukhov Tower on the Oka River is the world's only diagrid hyperboloid electricity pylon transmission tower. In 2009 one tower was illegally taken down to re-sell the metal. |
| Dorton Arena | 1952 | Raleigh, North Carolina | United States | Hyperbolic paraboloid saddle roof on arena | | Maciej Nowicki | |
| Transmitter Building of Europe 1 | 1954 | Überherrn | Germany | Hyperbolic paraboloid saddle roof | 16 m (52 ft) | | transmitter building of a 2000 kW longwave broadcasting transmitter |
| Fedala Reservoir | 1957 | Mohammedia | Morocco | Hyperboloid water tower | | Eduardo Torroja | |
| Ochsenkopf TV Tower | 1958 | Ochsenkopf | Germany | Hyperboloid broadcast tower | 163 m (535 ft) | | Radio and TV tower made of reinforced concrete. |
| Philips Pavilion | 1958 | Brussels, Belgium | Belgium | A cluster of nine hyperbolic paraboloid concrete roofs | | Le Corbusier | Commissioned by the Netherlands electronics company Philips, the pavilion at the World's Fair Expo '58 in Brussels was designed by Le Corbusier to house a multimedia spectacle that celebrated postwar technological progress. |
| Mürwik Wasserturm (Mürwik Water Tower) | 1961 | Flensburg | Germany | Hyperboloid water tower | | | |
| Warszawa Ochota railway station | 1962 | Warsaw | Poland | Hyperbolic paraboloid saddle roof on train station | | | |
| Church Army Chapel, Blackheath | 1963 | Blackheath, south east London | United Kingdom | Hyperbolic paraboloid saddle roof on church | | E.T. Spashett | |
| Kobe Port Tower | 1963 | Kōbe | Japan | Hyperboloid observation tower | 108 m (354 ft) | Nikken Sekkei Company | |
| Saint Louis Science Center's James S. McDonnell Planetarium | 1963 | St. Louis, Missouri | United States | Hyperboloid building museum planetarium | | Gyo Obata of Hellmuth, Obata and Kassabaum | |
| Möglingen Wasserturm (Möglingen Water Tower) | 1965 | Ludwigsburg | Germany | Hyperboloid water tower | | R. Kessler | |
| Święty Krzyż TV Tower | 1966 | Łysa Góra | Poland | Hyperboloid broadcast tower | 157 m (515 ft) | | |
| Water tower in Rishon LeZion | 1967 | Rishon LeZion | Israel | Hyperboloid water tower | 33.5 m (109.9 ft) | | |
| Newcastle International Airport air traffic control tower | 1967 | Newcastle upon Tyne | United Kingdom | Hyperboloid observation tower | | | |
| Cockfosters Water Tower | 1968 | London | United Kingdom | Hyperboloid water tower | | Edmund C. Percey of Scherrer and Hicks and J.W. Milne | Cockfosters Water Tower is in Cockfosters Road, north London, on the edge of Trent Park. |
| Ještěd Tower | 1968 | Liberec | Czech Republic | Hyperboloid broadcast tower | 94 m (308 ft) | Karel Hubáček | |
| Wrexham Swimming Baths, now the Wrexham Waterworld Leisure and Activity Centre | 1969 | Wrexham, Wales | United Kingdom | Hyperbolic paraboloid saddle roof on indoor swimming pool | | F.D. Williamson associates of Bridgend | |
| Cathedral of Brasília | 1970 | Brasília | Brazil | Hyperboloid building cathedral | 42 m (138 ft) | Oscar Niemeyer | |
| Scandinavium | 1971 | Gothenburg | Sweden | Hyperbolic paraboloid saddle roof on arena | | Poul Hultberg, for Nils Olsson's Gothenburg firm | |
| Ciechanów Water Tower | 1972 | Ciechanów | Poland | Hyperboloid water tower | | Jan Bogusławski, Jerzy Michał Bogusławski | A toroidal water tower tank on a doubly ruled hyperboloid structure. |
| Gettysburg National Tower | 1974-2000 | Gettysburg, Pennsylvania | United States | Hyperboloid observation tower | 120 m (390 ft) | Joel H. Rosenblatt | Demolished in 2000. |
| de:BIZ-Turm (BIS Tower) of the Bank for International Settlements | 1977 | Basel | Switzerland | Hyperboloid skyscraper tower | 69.5 m (228 ft) | Martin Burckhardt | Tower for the untouchables. |
| Sydney Tower | 1981 | Sydney | Australia | Hyperboloid observation tower | 309 m (1,014 ft) | Donald Crone, Australian | |
| Le Havre's House of Culture, a.k.a. fr:Le Volcan (salle) (The Volcano (hall/auditorium)) | 1982 | Le Havre | France | Hyperboloid building concert hall | | Oscar Niemeyer, Brazilian | |
| Roy Thomson Hall | 1982 | Toronto | Canada | Hyperboloid building concert hall | | Arthur Erickson and Mathers and Haldenby, Canadian | |
| Scotiabank Saddledome | 1983 | Calgary | Canada | Hyperbolic paraboloid saddle roof on indoor arena | | Graham McCourt Architects | |
| THTR-300 thorium nuclear reactor cooling tower | 1983 | Hamm-Uentrop | Germany | Hyperboloid cooling tower | 180 m (590 ft) | Schlaich Bergermann & Partner | The THTR-300 cable-net dry cooling tower for the now decommissioned thorium high-temperature nuclear reactor. |
| Canada Place | 1985 | Vancouver, British Columbia | Canada | Hyperbolic paraboloid saddle roofs in series with masts and fabric resembling sails | | Zeidler Roberts Partnership in joint venture with Musson Cattell Mackey Partnership and DA Architects + Planners. | Canada Place houses the Vancouver Convention Centre, the Pan Pacific Vancouver Hotel, Vancouver's World Trade Centre, the virtual flight ride FlyOver Canada, and is the main cruise ship terminal for the region. |
| Tractricious | 1988 | Fermilab, Batavia, Illinois | United States | Hyperboloid public art sculpture | | Robert R. Wilson | The Tractricious sculpture in front of Fermilab's Illinois Accelerator Research Center (IARC), Illinois, designed by Robert R. Wilson who derived the name Tractricious from tracktrix, a curve such that any tangent segment from the tangent point on the curve to the curve's asymptote have constant length, a concept first introduced by Claude Perrault in 1670. |
| Yangudun Radio and Television Tower | 1994 | Qingdao | China | Hyperboloid observation tower | 108 m (354 ft) | | |
| Corporation Street Bridge | 1999 | Manchester | United Kingdom | Hyperboloid building enclosed walkway | | Hodder + Partners | |
| Orion Tower | 2001 | Samara | Russia | Hyperboloid broadcast tower | 201 m (660 ft) | | Radio and TV steel lattice tower |
| Killesberg Tower | 2001 | Stuttgart | Germany | Hyperboloid observation tower | 40.4 m (133 ft) | Jörg Schlaich and Schlaich Bergermann Partner | Originally planned for the 1993 World Horticultural Exposition, it was only erected in 2001. |
| Aussichtsturm Schlossberg (Schlossberg View Tower) a.k.a. Castle Hill Tower | 2002 | Freiburg im Breisgau | Germany | Hyperboloid observation tower | 35 m (115 ft) | Hubert Horbach, Freiburg | |
| Hitachinaka Power Plant | 2003 | Hitachinaka | Japan | Hyperboloid smokestack | 230 m (754 ft) | | |
| Radio Mast at Krupskoi Street | 2003 | Perm | Russia | Hyperboloid broadcast tower | 180 m (591 ft) | | Radio and TV steel lattice tower |
| Messe Wien Turm / Messeturm (Vienna Trade Fair Tower / Exhibition-tower) | 2004 | Vienna | Austria | Hyperboloid public art sculpture decorative illuminated tower landmark | 63 m (207 ft) | Gustav Peichl, Rudolf F. Weber, Katharina Fröch, Christoph Lechner, Paul Katzberger, Gerhard Moßburger, Norbert Erlach | The largest trade fair in Austria and one of the most important economic factors of Vienna. |
| Barcelona–El Prat Airport air traffic control tower | 2005 | El Prat de Llobregat, near Barcelona | Spain | Hyperboloid observation tower | | Ricardo Bofill, Spanish | |
| Borůvka Tower | 2005 | Chrudim | Czech Republic | Hyperboloid observation tower | 18.5 m (61 ft) | Martin Novák and Antonín Olšina | |
| de:TBZ-Turm (TBZ Tower) | 2005 | Zürich | Switzerland | Hyperboloid observation tower | 13.3 m (47 ft) | Daniel Roth (artist), German | The winner of a 2003 competition had his tower built on the roof of the Zürich's Technical Vocational School. Initially accessible, the observation tower has been closed indefinitely due to student mischief. |
| Aspire Tower a.k.a. "The Torch Doha" | 2007 | Doha | Qatar | Hyperboloid skyscraper tower | 300 m (984 ft) | Hadi Simaan and AREP and engineer Ove Arup and Partners | |
| BMW Welt (BMW World) | 2007 | Munich | Germany | Hyperboloid building event venue and museum | | Viennese professor Wolf D. Prix and architect firm Coop Himmelb (l) au | |
| Tornado Tower a.k.a. the "QIPCO Tower" | 2008 | Doha | Qatar | Hyperboloid skyscraper tower | 195 m (640 ft) | | |
| de:Lörmecke-Turm (Lörmecke Tower) | 2008 | Warstein, Arnsberg, North Rhine-Westphalia | Germany | Hyperboloid observation tower | 35 m (115 ft) | Joh.-Ulrich Blecke and Dr. Ing. Michael Maas | |
| Slunečná Tower | 2009 | Velké Pavlovice | Czech Republic | Hyperboloid observation tower | 18.6 m (61 ft) | Ing. Martin Novák in cooperation with Antonín Olšina | |
| Canton Tower a.k.a. Guangzhou Tower | 2010 | Guangzhou | China | Hyperboloid skyscraper tower | 604 m (1,982 ft) | Dutch architects Mark Hemel and Barbara Kuit of Information Based Architecture, together with Arup, the international design, engineering and business consulting firm headquartered in London | The Canton Tower is in the Haizhu District of the city of Guangzhou (historically known as Canton), in Guangdong, China. |
| Ferrari World Abu Dhabi | 2010 | Yas Island in Abu Dhabi | United Arab Emirates | Hyperboloid building | | | the largest space frame structure ever built |
| de:Jübergturm (Jüberg Tower) | 2010 | de:Jüberg, Hemer, Märkischer Kreis, Arnsberg, North Rhine-Westphalia | Germany | Hyperboloid observation tower | 23.5 m (77 ft) | Beat Müller and Katharina Schewe, Swiss + Birk and Heilmeyer, Stuttgart | The first wooden hyperboloid tower structurally supported only by the outer wood framework. |
| Khan Shatyry Entertainment Center | 2010 | Khan Shatyr, Astana | Kazakhstan | Hyperboloid superstructure | 150 m (492 ft) | Norman Foster of Foster and Partners | The highest tensile structure in the world. |
| Lee Valley VeloPark a.k.a. London VeloPark | 2011 | Queen Elizabeth Olympic Park, East London | United Kingdom | Hyperbolic paraboloid saddle roof on cycling centre arena | | Hopkins Architects, Grant Associates | |
| Mae West (sculpture) | 2011 | Munich | Germany | Hyperboloid public art sculpture | 52 m (171 ft) | Rita McBride | |
| San Clan | 2012 | Tankwa Karoo National Park | South Africa | Hyperboloid public art sculpture tower | | | A temporary tower and ephemeral effigy constructed to intentionally burn in celebration at AfrikaBurn 2012, a Burning Man regional event. |
| Vysoká u Tachova Tower | 2014 | Tachov | Czech Republic | Hyperboloid observation tower | | Hysek architectural studio | |
| Perm TV Tower | 2016 | Perm | Russia | Hyperboloid broadcast tower | 275 m (902 ft) | | A radio and TV steel lattice tower |
| Warsaw Spire | 2016 | Warsaw | Poland | Hyperboloid skyscraper tower | 220 m (721 ft) | Jaspers-Eyers Architects and PROJEKT Polsko-Belgijska Pracownia Architektury | The Warsaw Spire is a complex of Neomodern office buildings in Warsaw, Poland. |
| Camp Adventure (observation tower and walkway) | 2018 | Gisselfeld Klosters forests, between Haslev and Næstved, | Denmark | Hyperboloid observation tower | 45 m (148 ft) | EFFEKT Architects | 45m spiral walkway. |
| Vakif Bank Headquarters Tower | 2023 | Istanbul Financial Center, Istanbul | Turkey | Hyperboloid skyscraper tower | 222 m (726 ft) | Tabanlıoğlu Architects | The Vakif Bank Headquarters Tower is a project of Istanbul Financial Center (IFC) office buildings in Istanbul, Turkey. |
| Les Essarts-le-Roi Château d'Eau (Les Essarts-le-Roi Water Tower) | | Les Essarts-le-Roi, Yvelines | France | Hyperboloid water tower | | | |
| Gen Coel Building | | Heerlerheide, Heerlen | Netherlands | Hyperboloid building public library, shopping, and community centre | | | Utilizes geothermal mine water ("Mijnwater") heating and cooling. See also: nl:Aardwarmte#Aardwarmte uit mijngangen. |
| Tempo (sculpture), a.k.a. Samspel (interaction/interplay/teamwork) | | Husnes | Norway | Hyperboloid public art sculpture | | LEADinc | Commissioned by Hydro Husnes, formerly Sør-Norge Aluminium AS. |
| Sagrada Família | | Barcelona | Spain | Hyperboloid building cathedral vaults and windows | | Antoni Gaudí | Under construction since 1882 with an estimated completion in 2026. |

### Notable Projects Never Built

| Structure | Location | Country | Function | Height | Architect | Notes |
| Burj Al Alam | Business Bay, Dubai | United Arab Emirates | Hyperboloid skyscraper tower | 510 m (1,670 ft) | Nikken Sekkei | Cancelled in 2013 |
| Crystal Island | Moscow | Russia | Hyperboloid superstructure | 450 m (1,476 ft) | Norman Foster of Foster and Partners | In 2009, due to the global economic crisis, financial backing for the project was lost, and construction of the project was postponed. |
| Vortex Tower | London | United Kingdom | Hyperboloid skyscraper tower | 300 m (984 ft) | Ken Shuttleworth | Designed in 2012 |

## Gallery of more hyperbolic paraboloid structures

* The hyperbolic paraboloid is a doubly ruled surface, and thus can be used to construct a saddle roof from straight beams.
* A saddle roof is a hyperbolic paraboloid, that mathematically, as a doubly ruled surface, can be constructed from two rows of straight beams.
* Pringles are examples of hyperbolic paraboloids.
* Stackable Pringles Chips.

## Gallery of more hyperboloid structures

* A hyperboloid of one sheet is a doubly ruled surface: it can be generated by either of two families of straight lines.
* Four images of hyperboloid towers.
* The Shukhov Tower in Polibino, the world's first hyperboloid structure, a water tower by Vladimir Shukhov at the All-Russian Exposition in Nizhny Novgorod, Russia
* The Shukhov Tower in Polibino
* A Carl Faberge miniature silver model replica of Shukhov Tower, in 1896.
* The Shukhov Tower in Moscow, Russia
* House of Culture, nicknamed "Le Volcan" by its Brazilian architect, Oscar Niemeyer, Le Havre, France, 1982
* The Corporation Street Bridge in Manchester, England
* BMW Welt, a museum and event venue at the Olympic Park, Munich, Germany, designed by Wolf D. Prix and architect firm Coop Himmelb(l)au
* The Canton Tower in Guangzhou, China
* The Khan Shatyr Entertainment Center, a daytime computer render on a postage stamp.
* The Vysoká Tower in Tachov, Czech Republic
* Shukhov's hyperpoloid water tower in Lobnya-Lugovaya near Moscow
* Shukhov water tower in Mykolaiv, Ukraine
* Space Needle, Seattle, United States
* Pseudosphaera statue in Târgu Mureş
* Our Zuo table
* 3D-printed dual-use pen/toothbrush holder-cup. Printed on Ultimaker 2
* Spaghetti spiral
* Hyperboloid metallic monument near Nagoya Station in Japan
* Vukovar water tower, Croatia

## Gallery of hyperboloid ship masts

* Hyperboloid mast towers were on Russian Andrei Pervozvanny-class battleships, like the "Imperator Pavel" (Emperor Paul I), early June 1912.
* Hyperboloid mast towers were on Andrei Pervozvanny-class battleships, like the Imperator Pavel I, underway, on this postcard circa 1917.
* Hyperboloid mast towers were on Andrei Pervozvanny-class battleships, illustrated plans from Brassey's Naval Annual 1912.
* Hyperboloid mast towers were on the USS Arizona, underway circa 1917–1929, prior to refitting in 1929.
* Hyperboloid mast towers were on the USS Arizona, a view from the Manhattan Bridge on the East River, in New York City, December 25, 1916.
* Hyperboloid mast towers were on the USS Arizona, passing the 96th St. Pier in New York City, circa December 26, 1918.
* Hyperboloid mast towers were on the USS Arizona, in lock, Panama, 1921.
* Hyperboloid mast towers were on the USS Arizona, with the ship's complement posing on her forecastle, forward turrets and superstructure, circa 1924.
* Hyperboloid mast towers were on the USS New Mexico, in 1921, prior to refitting in 1931.
* Hyperboloid mast towers were on the USS Oklahoma, at anchor wearing experimental camouflage, circa 1917, prior to refitting in 1927–1929.
* Hyperboloid mast towers were on the USS Oklahoma, under way during her sea trials, in "Popular Mechanics" Magazine, March 1916.
* Hyperboloid towers of USS Oklahoma, 1920.
* Hyperboloid mast towers were on the USS West Virginia, in San Francisco Bay circa 1934, prior to refitting in 1942–1944.
* Hyperboloid mast towers were on the USS West Virginia aflame at Pearl Harbor on December 7, 1941.
* Hyperboloid mast towers were on the USS West Virginia aflame at Pearl Harbor on December 7, 1941, and a small boat rescues a seaman.
* Hyperboloid towers of USS West Virginia, Pearl Harbor, 1941.