This page is a list of

hyperboloid structure Hyperboloid structures are architectural structures designed using a hyperboloid in one sheet. Often these are tall structures, such as towers, where the hyperboloid geometry's structural strength is used to support an object high above the grou ...

s. These were first applied in

architecture Architecture is the art and technique of designing and building, as distinguished from the skills associated with construction. It is both the process and the product of sketching, conceiving, planning, designing, and construction, constructi ...

by Russian engineer

Vladimir Shukhov Vladimir Grigoryevich Shukhov (; – 2 February 1939) was a Russian and Soviet engineer-polymath, scientist and architect renowned for his pioneering works on new methods of analysis for structural engineering that led to breakthroughs in indu ...

(1853–1939). Shukhov built his first example as a water tower (

hyperbolic Hyperbolic may refer to: * of or pertaining to a hyperbola, a type of smooth curve lying in a plane in mathematics ** Hyperbolic geometry, a non-Euclidean geometry ** Hyperbolic functions, analogues of ordinary trigonometric functions, defined u ...

shell Shell may refer to: Architecture and design * Shell (structure), a thin structure ** Concrete shell, a thin shell of concrete, usually with no interior columns or exterior buttresses Science Biology * Seashell, a hard outer layer of a marine ani ...

) for the 1896 All-Russian Exposition. Subsequently, more have been designed by other architects, including

Le Corbusier Charles-Édouard Jeanneret (6 October 188727 August 1965), known as Le Corbusier ( , ; ), was a Swiss-French architectural designer, painter, urban planner and writer, who was one of the pioneers of what is now regarded as modern architecture ...

Antoni Gaudí Antoni Gaudí i Cornet ( , ; ; 25 June 1852 – 10 June 1926) was a Catalans, Catalan architect and designer from Spain, widely known as the greatest exponent of Catalan ''Modernisme''. Gaudí's works have a style, with most located in Barc ...

Eduardo Torroja Eduardo Torroja y Miret, 1st Marques of Torroja (27 August 1899 – 15 June 1961) was a Spanish structural engineer and a pioneer in the design of concrete shell structures. Education Torroja was born in Madrid where he studied civil engineerin ...

Oscar Niemeyer Oscar Ribeiro de Almeida Niemeyer Soares Filho (15 December 1907 – 5 December 2012), known as Oscar Niemeyer (), was a Brazilian architect considered to be one of the key figures in the development of modern architecture. Niemeyer was b ...

and Ieoh Ming Pei. The shapes are

doubly ruled surface In geometry, a surface in 3-dimensional Euclidean space is ruled (also called a scroll) if through every point of , there is a straight line that lies on . Examples include the plane, the lateral surface of a cylinder or cone, a conical surfa ...

s, which can be classed as: *

Hyperbolic paraboloid In geometry, a paraboloid is a quadric surface that has exactly one axis of symmetry and no center of symmetry. The term "paraboloid" is derived from parabola, which refers to a conic section that has a similar property of symmetry. Every pla ...

s, such as

saddle roof A saddle roof is a roof form which follows a convex curve about one axis and a concave curve about the other. The hyperbolic paraboloid form has been used for roofs at various times since it is easily constructed from straight sections of lumber, ...

s *

Hyperboloid of one sheet In geometry, a hyperboloid of revolution, sometimes called a circular hyperboloid, is the surface (mathematics), surface generated by rotating a hyperbola around one of its Hyperbola#Equation, principal axes. A hyperboloid is the surface obtained ...

, such as

cooling tower A cooling tower is a device that rejects waste heat to the atmosphere through the cooling of a coolant stream, usually a water stream, to a lower temperature. Cooling towers may either use the evaporation of water to remove heat and cool the ...

s Image:Ruled hyperboloid.jpg, A

hyperboloid In geometry, a hyperboloid of revolution, sometimes called a circular hyperboloid, is the surface generated by rotating a hyperbola around one of its principal axes. A hyperboloid is the surface obtained from a hyperboloid of revolution by def ...

of one sheet is a

, and it may be generated by either of two families of straight lines. Image:Hyperbolic-paraboloid.jpg, The

hyperbolic paraboloid In geometry, a paraboloid is a quadric surface that has exactly one axis of symmetry and no center of symmetry. The term "paraboloid" is derived from parabola, which refers to a conic section that has a similar property of symmetry. Every pla ...

is a

so it may be used to construct a

from straight beams.

Notable projects

Notable Projects Never Built

Gallery of more hyperbolic paraboloid structures

Image:Hyperbolic-paraboloid.svg, The

is a

, and thus can be used to construct a

from straight beams. Image:Hyperbolic-paraboloid.jpg, A

is a

, that mathematically, as a

, can be constructed from two rows of straight beams. Image:Pringles chips.JPG,

Pringles Pringles is an American brand of stackable potato-based chips invented by Procter & Gamble (P&G) in 1968 and marketed as "Pringle's Newfangled Potato Chips". It is technically considered an Extruded food, extruded snack because of the manufac ...

are examples of hyperbolic paraboloids. Image:Stapelchips.jpg, Stackable Pringles Chips.

Gallery of more hyperboloid structures

Ruled hyperboloid.jpg, A

of one sheet is a doubly ruled surface: it can be generated by either of two families of straight lines. Four hyperboloid towers.jpg, Four images of hyperboloid towers. First Shukhov Tower Nizhny Novgorod 1896.jpg, The

Shukhov Tower in Polibino The Shukhov Tower in Polibino, designed in 1896 by Russian engineer and architect Vladimir Shukhov, is the world's first diagrid hyperboloid structure. The tower is today located in the former estate of Yury Nechaev-Maltsov in the selo of P ...

, the world's first

, a water tower by

at the All-Russian Exposition in

Nizhny Novgorod Nizhny Novgorod ( ; rus, links=no, Нижний Новгород, a=Ru-Nizhny Novgorod.ogg, p=ˈnʲiʐnʲɪj ˈnovɡərət, t=Lower Newtown; colloquially shortened to Nizhny) is a city and the administrative centre of Nizhny Novgorod Oblast an ...

, Russia Worlds First Hyperboloid in Polibino photo by Arssenev.jpg, The

Worlds First hyperboloid Shukhov Tower by Faberge.jpg, A Carl Faberge miniature silver model replica of

Shukhov Tower The Shukhov Radio Tower (), also known as the Shabolovka Tower (), is a broadcasting tower deriving from the Russian avant-garde in Moscow designed by Vladimir Shukhov. The free-standing steel diagrid structure was built between 1920 and 19 ...

, in 1896. Shukhov Tower photo by Maxim Fedorov. Night.jpg, The

Moscow Moscow is the Capital city, capital and List of cities and towns in Russia by population, largest city of Russia, standing on the Moskva (river), Moskva River in Central Russia. It has a population estimated at over 13 million residents with ...

, Russia Le Havre, the City Rebuilt by Auguste Perret-113542.jpg, ''House of Culture'', nicknamed "Le Volcan" by its Brazilian architect,

, Le Havre, France, 1982 Bridge over Corporation Street - geograph.org.uk - 809089.jpg, The Corporation Street Bridge in

Manchester Manchester () is a city and the metropolitan borough of Greater Manchester, England. It had an estimated population of in . Greater Manchester is the third-most populous metropolitan area in the United Kingdom, with a population of 2.92&nbs ...

, England Musée BMW 007.jpg,

BMW Welt The BMW Welt is a combined exhibition, delivery, adventure museum, and event venue located in Munich's district Am Riesenfeld, next to the Olympiapark (Munich), Olympic Park, in the immediate vicinity of the BMW Headquarters and factory. It was ...

, a museum and event venue at the

Olympic Park An Olympic Park is a sports campus for hosting the Olympic Games. Typically it contains the Olympic Stadium and the International Broadcast Centre. It may also contain the Olympic Village or some of the other sports venues, such as the aquatics ...

Munich Munich is the capital and most populous city of Bavaria, Germany. As of 30 November 2024, its population was 1,604,384, making it the third-largest city in Germany after Berlin and Hamburg. Munich is the largest city in Germany that is no ...

, Germany, designed by

Wolf D. Prix Wolf Dieter Prix is an Austrian architect. In 1968 he co-founded the architects' cooperative Coop Himmelb(l)au, which has an international reputation as an important representative of deconstructivism. Life Early life Wolf Prix's father ...

and architect firm

Coop Himmelb(l)au Coop Himmelb(l)au (a pun meaning '' Coop Sky Building'' and ''Coop Sky Blue'') is an architecture, urban planning, design and art firm founded in 1968 by Wolf D. Prix, Helmut Swiczinsky and Michael Holzer in Vienna, Austria. History Coop Hi ...

Guangzhou Tower.jpg, The

Canton Tower The Canton Tower (), formally Guangzhou TV Astronomical and Sightseeing Tower (), is a -tall multipurpose observation tower in the Haizhu District of Guangzhou (Postal Map Romanization, alternatively romanized as ''Canton''). The tower was Top ...

Guangzhou Guangzhou, Chinese postal romanization, previously romanized as Canton or Kwangchow, is the Capital city, capital and largest city of Guangdong Provinces of China, province in South China, southern China. Located on the Pearl River about nor ...

, China Stamps of Kazakhstan, 2010-08.jpg, The

Khan Shatyr Entertainment Center Khan Shatyr () is a transparent tent-shaped Entertainment Center located in Astana, the capital city of Kazakhstan. Built in a neo-futurist style, the architectural project was unveiled by the first President of Kazakhstan Nursultan Nazarbayev o ...

, a daytime computer render on a

postage stamp A postage stamp is a small piece of paper issued by a post office, postal administration, or other authorized vendors to customers who pay postage (the cost involved in moving, insuring, or registering mail). Then the stamp is affixed to the f ...

. Tachov - rozhledna Vysoká (1).JPG, The Vysoká Tower in

Tachov Tachov (; ) is a town in the Plzeň Region of the Czech Republic. It has about 14,000 inhabitants. It lies on the Mže River. The historic town centre is well preserved and is protected as an urban monument zone. Administrative division Tachov ...

, Czech Republic Водонапорная башня в поселке Луговая.JPG, Shukhov's hyperpoloid water tower in Lobnya-Lugovaya near

Shuhov tower Nikolaev.jpg, Shukhov water tower in

Mykolaiv Mykolaiv ( ), also known as Nikolaev ( ) is a List of cities in Ukraine, city and a hromada (municipality) in southern Ukraine. Mykolaiv is the Administrative centre, administrative center of Mykolaiv Raion (Raions of Ukraine, district) and Myk ...

, Ukraine Space Needle 2011-07-04.jpg,

Space Needle The Space Needle is an observation tower in Seattle, Washington, United States. Considered to be an icon of the city, it has been designated a List of Seattle landmarks, Seattle landmark. Located in the Lower Queen Anne, Seattle, Lower Queen An ...

Seattle Seattle ( ) is the most populous city in the U.S. state of Washington and in the Pacific Northwest region of North America. With a population of 780,995 in 2024, it is the 18th-most populous city in the United States. The city is the cou ...

, United States Pseudosphaera1.jpg, Pseudosphaera statue in

Târgu Mureş Târgu (Romanian language, Romanian for "the market") starts off the names of several places in Romania: *Târgu Bujor *Târgu Cărbunești *Târgu Frumos *Berbești, Târgu Gânguleşti *Târgu Jiu *Târgu Lăpuș *Logrești, Târgu Logreşti *Tâ ...

Our Zuo table.jpg, Our Zuo table 3D dual use.jpg,

3D-printed 3D printing, or additive manufacturing, is the Manufacturing, construction of a three-dimensional object from a computer-aided design, CAD model or a digital 3D modeling, 3D model. It can be done in a variety of processes in which material i ...

dual-use pen/toothbrush holder-cup. Printed on Ultimaker 2 Spaghetti spiral, 2008.jpg,

Spaghetti Spaghetti () is a long, thin, solid, cylindrical pasta.spaghetti
Dictionary.com. Dictionary.com Una ...

spiral Nagoya Station (1043).JPG, Hyperboloid metallic monument near

Nagoya is the largest city in the Chūbu region of Japan. It is the list of cities in Japan, fourth-most populous city in Japan, with a population of 2.3million in 2020, and the principal city of the Chūkyō metropolitan area, which is the List of ...

Station in Japan Vukovar-watertower-after-war.jpg,

Vukovar Vukovar (; sr-Cyrl, Вуковар, , ) is a city in Croatia, in the eastern Regions of Croatia, regions of Syrmia and Slavonia. It contains Croatia's largest river port, located at the confluence of the Vuka (river), Vuka and the Danube. Vukova ...

water tower, Croatia

Gallery of hyperboloid ship masts

Image:Imperator Pavel battleship.jpg, Hyperboloid mast towers were on Russian ''Andrei Pervozvanny''-class battleships, like the "Imperator Pavel" (Emperor Paul I), early June 1912. Image:ImperatorPavel-postcard.jpg, Hyperboloid mast towers were on ''Andrei Pervozvanny''-class battleships, like the Imperator Pavel I, underway, on this postcard circa 1917. Image:Pervozvanny class diagrams Brasseys 1912.jpg, Hyperboloid mast towers were on ''Andrei Pervozvanny''-class battleships, illustrated plans from

Brassey's Naval Annual ''The Naval Annual'' was a Periodical literature, periodical that provided considerable text and graphic information (largely concerning the British Royal Navy) which had previously been obtainable only by consulting a wide range of often foreign ...

1912. Image:Arizona (BB39) Port Bow, Underway - NARA - 5900075 - 1930.jpg, Hyperboloid mast towers were on the , underway circa 1917–1929, prior to refitting in 1929. Image:USS Arizona in New York City Crisco edit.jpg, Hyperboloid mast towers were on the , a view from the

Manhattan Bridge The Manhattan Bridge is a suspension bridge that crosses the East River in New York City, connecting Lower Manhattan at Canal Street with Downtown Brooklyn at the Flatbush Avenue Extension. Designed by Leon Moisseiff, the bridge has a tota ...

on the

East River The East River is a saltwater Estuary, tidal estuary or strait in New York City. The waterway, which is not a river despite its name, connects Upper New York Bay on its south end to Long Island Sound on its north end. It separates Long Island, ...

, in

New York City New York, often called New York City (NYC), is the most populous city in the United States, located at the southern tip of New York State on one of the world's largest natural harbors. The city comprises five boroughs, each coextensive w ...

, December 25, 1916. Image:USS Arizona (BB-39) 1918.jpg, Hyperboloid mast towers were on the , passing the 96th St. Pier in

, circa December 26, 1918. Image:U.S.S. Arizona in lock, Panama.jpg, Hyperboloid mast towers were on the , in lock,

Panama Panama, officially the Republic of Panama, is a country in Latin America at the southern end of Central America, bordering South America. It is bordered by Costa Rica to the west, Colombia to the southeast, the Caribbean Sea to the north, and ...

, 1921. Image:USS Arizona (BB-39) - NH 86101.jpg, Hyperboloid mast towers were on the , with the ship's complement posing on her forecastle, forward turrets and superstructure, circa 1924. Image:USS New Mexico BB-40 1921.jpg, Hyperboloid mast towers were on the , in 1921, prior to refitting in 1931. Image:USS Oklahoma BB-37.jpg, Hyperboloid mast towers were on the , at anchor wearing experimental

camouflage Camouflage is the use of any combination of materials, coloration, or illumination for concealment, either by making animals or objects hard to see, or by disguising them as something else. Examples include the leopard's spotted coat, the b ...

, circa 1917, prior to refitting in 1927–1929. Image:USS Oklahoma (BB-37) sea trials 1916.JPG, Hyperboloid mast towers were on the , under way during her sea trials, in "

Popular Mechanics ''Popular Mechanics'' (often abbreviated as ''PM'' or ''PopMech'') is a magazine of popular science and technology, featuring automotive, home, outdoor, electronics, science, do it yourself, and technology topics. Military topics, aviation an ...

" Magazine, March 1916. Image:Uss oklahoma bb.jpg, Hyperboloid towers of , 1920. Image:Uss west virginia bb.jpg, Hyperboloid mast towers were on the , in

San Francisco Bay San Francisco Bay (Chochenyo language, Chochenyo: 'ommu) is a large tidal estuary in the United States, U.S. state of California, and gives its name to the San Francisco Bay Area. It is dominated by the cities of San Francisco, California, San ...

circa 1934, prior to refitting in 1942–1944. Image:USS WEST VIRGINIA aflame Nara 80-G-19947.png, Hyperboloid mast towers were on the aflame at

Pearl Harbor Pearl Harbor is an American lagoon harbor on the island of Oahu, Hawaii, west of Honolulu. It was often visited by the naval fleet of the United States, before it was acquired from the Hawaiian Kingdom by the U.S. with the signing of the Reci ...

on December 7, 1941. Image:USS West Virginia2.jpg, Hyperboloid mast towers were on the aflame at

on December 7, 1941, and a small boat rescues a seaman. Image:USS West Virginia sunk-Pearl Harbor-7Dec41.jpg, Hyperboloid towers of ,

, 1941.

Notes

{{DEFAULTSORT:List Of Hyperboloid Structures Structural system Hyperboloid structures

Notable projects

Notable Projects Never Built

Gallery of more hyperbolic paraboloid structures

Gallery of more hyperboloid structures

Gallery of hyperboloid ship masts

See also

Notes