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
	1957	Mohammedia	Morocco	Hyperboloid water tower		Eduardo Torroja	[1]
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.
Pylons of Cádiz	1960	Cádiz	Spain	Hyperboloid electricity pylon towers	158 m (518 ft)	Alberto Toscano, Italian	The Pylons of Cádiz, (aka Towers of Cádiz), are two tall electricity pylon supporting powerlines over the bay of Cádiz, Spain.
Mürwik Wasserturm (Mürwik Water Tower)	1961	Flensburg	Germany	Hyperboloid water tower			[2]
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
Kobe Port Tower	1963	Kōbe	Japan	Hyperboloid observation tower	108 m (354 ft)
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
Święty Krzyż TV Tower	1966	Łysa Góra	Poland	Hyperboloid broadcast tower	157 m (515 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 and	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		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		,	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)		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)	, 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	[3]
Roy Thomson Hall	1982	Toronto	Canada	Hyperboloid building concert hall		Arthur Erickson and , Canadian
Scotiabank Saddledome	1983	Calgary	Canada	Hyperbolic paraboloid saddle roof on indoor arena
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 and DA Architects + Planners.	Canada Place houses the Vancouver Convention Centre, the Pan Pacific Vancouver Hotel, , 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 (IARC), Illinois, designed by Robert R. Wilson^[1]^[2] who derived the name Tractricious from , 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^[3]	1994^{[citation needed]}	Qingdao	China	Hyperboloid observation tower	108 m (354 ft)
Corporation Street Bridge	1999	Manchester	United Kingdom	Hyperboloid building enclosed walkway		Hodder + Partners
Orion Tower^[4]^[5]	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)	, Freiburg
Hitachinaka Power Plant^[6]	2003	Hitachinaka	Japan	Hyperboloid smokestack	230 m (754 ft)^[7]
Radio Mast at Krupskoi Street^[8]	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, , , , , ,	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	^[9]
cs:Borůvka (rozhledna) (Blueberry (lookout tower))	2005	Chrudim	Czech Republic	Hyperboloid observation tower	18.5 m (61 ft)	and	^[10]^[11]
de:TBZ-Turm (TBZ Tower)	2005	Zürich	Switzerland	Hyperboloid observation tower	13.3 m (47 ft)	, 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.
Moscow Octod Tower	2006	Moscow	Russia	Hyperboloid broadcast tower	258 m (846 ft)		A radio and TV steel lattice tower
Aspire Tower a.k.a. "The Torch Doha"	2007	Doha	Qatar	Hyperboloid skyscraper tower	300 m (984 ft)	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
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
cs:Slunečná (rozhledna) (Sunny (lookout lower))	2009	Velké Pavlovice	Czech Republic	Hyperboloid observation tower	18.6 m (61 ft)	Ing. in cooperation with
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.^[12]
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 , Swiss + , 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,
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.
Tachov Vysoká (Tachov High Lookout (Tower))	2014	Tachov	Czech Republic	Hyperboloid observation tower		architectural studio	^[13]^[14]
Perm TV Tower^[15]	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)	and	The Warsaw Spire is a complex of Neomodern office buildings in Warsaw, Poland.
	2018	Gisselfeld Klosters forests, between Haslev and Næstved,	Denmark	Hyperboloid observation tower	45 m (148 ft)		45m spiral walkway.^[16]^[17]^[18]^[19]
Les Essarts-le-Roi Château d'Eau (Les Essarts-le-Roi Water Tower)		Les Essarts-le-Roi, Yvelines	France	Hyperboloid water tower
		Heerlerheide, Heerlen	Netherlands	Hyperboloid building public library, shopping, and community centre			Utilizes geothermal mine water ("Mijnwater") heating and cooling.^[20] See also: nl:Aardwarmte#Aardwarmte uit mijngangen.
, a.k.a. (interaction/interplay/teamwork)		Husnes	Norway	Hyperboloid public art sculpture			Commissioned by Hydro Husnes, formerly .^[21]^[22]^[23]
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
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, 1896.
The Shukhov Tower in Polibino in 2006.
The Shukhov Tower in Polibino in 2009.
The Shukhov Tower in Polibino, interior view of the lattice hyperboloid structure, in 2009.
A Carl Faberge miniature silver model replica of Vladimir Shukhov's Tower, in 1896.
The Shukhov Tower, 1922, is currently under threat of demolition unless the international campaign can save it.
The Shukhov Tower, Moscow, Russia, at night in 2007.
House of Culture, nicknamed "Le Volcan" (The Volcano) by its Brazilian architect, Oscar Niemeyer, Le Havre, France, 1982.
House of Culture, nicknamed "Le Volcan" (The Volcano) by its Brazilian architect, Oscar Niemeyer, Le Havre, France, 1982.
The Corporation Street Bridge in Manchester, England, 1999.
The Corporation Street Bridge interior view.
BMW Welt, (BMW World), is a museum and event venue at the Olympic Park, Milbertshofen-Am Hart, Munich, Germany, designed by Viennese professor Wolf D. Prix and architect firm , 2007.
BMW Welt at night.
BMW Welt with the Olympiaturm (Olympic Tower) observation tower, dusk.
A wide view of the BMW World museum building.
The Canton Tower, looking up on 2010-10-01.
The Canton Tower, in the Haizhu District of the city of Guangzhou (historically known as Canton), in Guangdong, China, 2010.
The Canton Tower, at night in 2013.
The Khan Shatyr Entertainment Center, a daytime computer render on a postage stamp.
The Vysoká (High Lookout) Tower in the town of Tachov in the Pilsen Region, Czech Republic, 2014.
Vysoká observation tower, Tachov.
Shukhov's hyperpoloid water tower in Lobnya-Lugovaya near Moscow
Shukhov water tower in Mykolaiv, Mykolaiv Oblast, Ukraine.
Another view of the Shukhov water tower in Mykolaiv, Ukraine.
Space Needle, Seattle, United States, 1961.
Art exhibit in historic district of Longview, Texas, United States.
Pseudosphaera statue in Târgu Mureş
Our Zuo table.
3D-printed dual-use pen/toothbrush holder-cup. Printed on Ultimaker 2, 2015.
3D-printed dual-use pen/toothbrush holder-cup with samples removing support material. Printed on Ultimaker 2, 2015.
Spaghetti spiral, 2008.
Hyperboloid metallic monument near Nagoya Station in Japan.
Ruines du château d'eau de Vukovar (Croatie).

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.