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 constructing buildings ...

by Russian engineer

Vladimir Shukhov Vladimir Grigoryevich Shukhov (russian: link=no, Влади́мир Григо́рьевич Шу́хов; – 2 February 1939) was a Russian Empire and Soviet engineer-polymath, scientist and architect renowned for his pioneering works on new ...

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

hyperbolic Hyperbolic is an adjective describing something that resembles or pertains to a hyperbola (a curve), to hyperbole (an overstatement or exaggeration), or to hyperbolic geometry. The following phenomena are described as ''hyperbolic'' because they ...

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 ** Thin-shell structure Science Biology * Seashell, a hard o ...

) 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 architect, designer, painter, urban planner, writer, and one of the pioneers of what is now regarded as modern architecture. He was ...

Antoni Gaudí Antoni Gaudí i Cornet (; ; 25 June 1852 – 10 June 1926) was a Catalan architect from Spain known as the greatest exponent of Catalan Modernism. Gaudí's works have a highly individualized, ''sui generis'' style. Most are located in Barcel ...

, Eduardo Torroja,

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 ...

and

Ieoh Ming Pei Ieoh Ming Pei
– website of Pei Cobb Freed & Partners ( ; ; April 26, 1917 – May 16, 2019) was ...

. The shapes are doubly ruled surfaces, 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 plan ...

s, such as saddle roofs *

Hyperboloid of one sheet 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 ...

, 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 process heat an ...

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 doubly ruled surface, 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 plan ...

is a doubly ruled surface so it may be used to construct a saddle roof from straight beams.

Notable projects

Notable Projects Never Built

Gallery of more hyperbolic paraboloid structures

Image:Hyperbolic-paraboloid.svg, The

is a doubly ruled surface, and thus can be used to construct a saddle roof from straight beams. Image:Hyperbolic-paraboloid.jpg, A saddle roof is a

, that mathematically, as a doubly ruled surface, can be constructed from two rows of straight beams. Image:Pringles chips.JPG,

Pringles Pringles is an American brand of stackable potato-based crisps. Originally sold by Procter & Gamble (P&G) in 1968 and marketed as "Pringle's Newfangled Potato Chips", the brand was sold in 2012 to the current owner, Kellogg's. As of 2011, Pri ...

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

Gallery of more hyperboloid structures

Image:Ruled hyperboloid.jpg, A

of one sheet is a doubly ruled surface: it can be generated by either of two families of straight lines. Image:Four hyperboloid towers.jpg, Four images of hyperboloid towers. Image:First Shukhov Tower Nizhny Novgorod 1896.jpg, The Shukhov Tower in Polibino, 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 ), colloquially shortened to Nizhny, from the 13th to the 17th century Novgorod of the Lower Land, formerly known as Gork ...

Russia Russia (, , ), or the Russian Federation, is a transcontinental country spanning Eastern Europe and Northern Asia. It is the largest country in the world, with its internationally recognised territory covering , and encompassing one-ei ...

, 1896. Image:World First 1896 Hyperboloid Structure by Vladimir Shukhov in 2006.jpg, The Shukhov Tower in Polibino in 2006. Image:Worlds First Hyperboloid in Polibino photo by Arssenev.jpg, The Shukhov Tower in Polibino in 2009. Image:Worlds First Hyperboloid structure photo by Sergei Arssenev.jpg, The Shukhov Tower in Polibino, interior view of the lattice

, in 2009. Image:Worlds First hyperboloid Shukhov Tower by Faberge.jpg, A Carl Faberge miniature silver model replica of

Tower A tower is a tall structure, taller than it is wide, often by a significant factor. Towers are distinguished from masts by their lack of guy-wires and are therefore, along with tall buildings, self-supporting structures. Towers are specific ...

, in 1896. Image:Shukhov tower shabolovka moscow 02.jpg, The Shukhov Tower, 1922, is currently under threat of demolition unless the international campaign can save it. Image:Shukhov Tower photo by Maxim Fedorov. Night.jpg, The Shukhov Tower,

Moscow Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 million ...

, at night in 2007. Image:Le Volcan du Havre.jpg, ''House of Culture'', nicknamed "Le Volcan" (The Volcano) by its Brazilian architect,

, Le Havre, France, 1982. Image:Le Havre, the City Rebuilt by Auguste Perret-113542.jpg, ''House of Culture'', nicknamed "Le Volcan" (The Volcano) by its Brazilian architect,

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

Manchester Manchester () is a city in Greater Manchester, England. It had a population of 552,000 in 2021. It is bordered by the Cheshire Plain to the south, the Pennines to the north and east, and the neighbouring city of Salford to the west. The ...

England England is a country that is part of the United Kingdom. It shares land borders with Wales to its west and Scotland to its north. The Irish Sea lies northwest and the Celtic Sea to the southwest. It is separated from continental Europe ...

, 1999. Image:Arndale Bridge interior.jpg, The Corporation Street Bridge interior view. Image:München - BMW-Welt.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 Olympic Park, in the immediate vicinity of the BMW Headquarters and factory. It was built from August 200 ...

, (BMW World), is 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 ...

Milbertshofen-Am Hart Milbertshofen (Central Bavarian: ''Muibatshofa''), Am Riesenfeld and Am Hart (Central Bavarian: ''Am Hoart'') are three boroughs situated in the north of Munich in Germany. Jointly, they form the city district 11 Milbertshofen-Am Hart. , t ...

Munich Munich ( ; german: München ; bar, Minga ) is the capital and most populous city of the German state of Bavaria. With a population of 1,558,395 inhabitants as of 31 July 2020, it is the third-largest city in Germany, after Berlin and ...

Germany Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwee ...

, designed by

Viennese Viennese may refer to: * Vienna, the capital of Austria * Viennese people, List of people from Vienna * Viennese German, the German dialect spoken in Vienna * Music of Vienna, musical styles in the city * Viennese Waltz, genre of ballroom dance * ...

professor Wolf D. Prix and architect firm Coop Himmelb (l) au, 2007. Image:BMW-Welt at night 2.JPG, BMW Welt at night. Image:BMWwelt2014.jpg, BMW Welt with the

Olympiaturm The Olympic Tower (German: ) in the Olympic Park, Munich has an overall height of and a weight of 52,500 tons. At a height of there is an observation platform as well as an exhibition commemorating the 50th Anniversary of the Tower. Previousl ...

(Olympic Tower) observation tower, dusk. Image:Musée BMW 007.jpg, A wide view of the BMW World museum building. Image:Canton Tower(Look up).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 ( alternatively romanized as ''Canton''). The tower was topped out in 2009 and it ...

, looking up on 2010-10-01. Image:Guangzhou Tower.jpg, The

, in the

Haizhu District Haizhu District is one of 11 urban districts of the prefecture-level city of Guangzhou, the capital of Guangdong Province, China. Geography Haizhu District is located in the southern part of Guangzhou city. After the adjustment of Guangzhou's ...

of the city of

Guangzhou Guangzhou (, ; ; or ; ), also known as Canton () and Chinese postal romanization, alternatively romanized as Kwongchow or Kwangchow, is the Capital city, capital and largest city of Guangdong Provinces of China, province in South China, sou ...

(historically known as Canton), in

Guangdong Guangdong (, ), alternatively romanized as Canton or Kwangtung, is a coastal province in South China on the north shore of the South China Sea. The capital of the province is Guangzhou. With a population of 126.01 million (as of 2020 ...

China China, officially the People's Republic of China (PRC), is a country in East Asia. It is the world's List of countries and dependencies by population, most populous country, with a Population of China, population exceeding 1.4 billion, slig ...

, 2010. Image:Canton Tower 2013.11.15 18-12-45.jpg, The

, at night in 2013. , The

Khan Shatyr Entertainment Center Khan Shatyr ( kk, Хан Шатыр, Han Şatyr, Royal Marquee) is a transparent tent 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 Nu ...

at dusk. , The

and shopping mall, the highest tensile structure in the world, Khan Shatyr,

Astana Astana, previously known as Akmolinsk, Tselinograd, Akmola, and most recently Nur-Sultan, is the capital city of Kazakhstan. The city lies on the banks of the Ishim River in the north-central part of Kazakhstan, within the Akmola Region, tho ...

Kazakhstan Kazakhstan, officially the Republic of Kazakhstan, is a transcontinental country located mainly in Central Asia and partly in Eastern Europe. It borders Russia to the north and west, China to the east, Kyrgyzstan to the southeast, Uzbeki ...

, 2010. , The

and shopping mall. , The

and shopping mall, interior. , The

and shopping mall, interior. Image:Stamps of Kazakhstan, 2010-08.jpg, The

, 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), who then affix the stamp to the f ...

. Image:Tachov - rozhledna Vysoká (1).JPG, The Vysoká (High Lookout) Tower in the town of

Tachov Tachov (; german: Tachau) is a town in the Plzeň Region of the Czech Republic. It has about 13,000 inhabitants. It lies on the Mže River. The town centre is well preserved and is protected by law as an urban monument zone. Administrative parts ...

in the Pilsen Region,

Czech Republic The Czech Republic, or simply Czechia, is a landlocked country in Central Europe. Historically known as Bohemia, it is bordered by Austria to the south, Germany to the west, Poland to the northeast, and Slovakia to the southeast. The ...

, 2014. Image:Tachov - rozhledna Vysoká (2).JPG, Vysoká observation tower,

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

File:Shuhov tower Nikolaev.jpg, Shukhov water tower in

Mykolaiv Mykolaiv ( uk, Миколаїв, ) is a city and municipality in Southern Ukraine, the administrative center of the Mykolaiv Oblast. Mykolaiv city, which provides Ukraine with access to the Black Sea, is the location of the most downriver brid ...

Mykolaiv Oblast Mykolaiv Oblast ( uk, Микола́ївська о́бласть, translit=Mykoláyivsʹka óblastʹ, ), also referred to as Mykolaivshchyna ( uk, Микола́ївщина, Mykoláivshchyna, ) is an oblast (province) of Ukraine. The administra ...

Ukraine Ukraine ( uk, Україна, Ukraïna, ) is a country in Eastern Europe. It is the second-largest European country after Russia, which it borders to the east and northeast. Ukraine covers approximately . Prior to the ongoing Russian inva ...

. File:Shukhov tower in Nikolayev.jpg, Another view of the Shukhov water tower in

. File: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 Seattle landmark. Located in the Lower Queen Anne neighborhood, it was built in the Seattle Cente ...

Seattle Seattle ( ) is a seaport city on the West Coast of the United States. It is the seat of King County, Washington. With a 2020 population of 737,015, it is the largest city in both the state of Washington and the Pacific Northwest region o ...

United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country Continental United States, primarily located in North America. It consists of 50 U.S. state, states, a Washington, D.C., ...

, 1961. , Art exhibit in historic district of Longview,

Texas Texas (, ; Spanish: ''Texas'', ''Tejas'') is a state in the South Central region of the United States. At 268,596 square miles (695,662 km2), and with more than 29.1 million residents in 2020, it is the second-largest U.S. state by ...

. File:Pseudosphaera1.jpg, Pseudosphaera statue in

Târgu Mureş Târgu (Romanian for "the market") starts off the names of several places in Romania: * Târgu Bujor * Târgu Cărbunești * Târgu Frumos * Târgu Gânguleşti *Târgu Jiu * Târgu Lăpuș * Târgu Logreşti * Târgu Mureș *Târgu Neamț * Târgu ...

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

3D-printed 3D printing or additive manufacturing is the construction of a three-dimensional object from a CAD model or a digital 3D model. It can be done in a variety of processes in which material is deposited, joined or solidified under computer co ...

dual-use pen/toothbrush holder-cup. Printed on Ultimaker 2, 2015. File:Stützmaterial entfernen.jpg,

dual-use pen/toothbrush holder-cup with samples removing support material. Printed on Ultimaker 2, 2015. File:Spaghetti spiral, 2008.jpg,

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

spiral, 2008. File:Nagoya Station (1043).JPG, Hyperboloid metallic monument near

Nagoya is the largest city in the Chūbu region, the fourth-most populous city and third most populous urban area in Japan, with a population of 2.3million in 2020. Located on the Pacific coast in central Honshu, it is the capital and the most po ...

Station in

Japan Japan ( ja, 日本, or , and formally , ''Nihonkoku'') is an island country in East Asia. It is situated in the northwest Pacific Ocean, and is bordered on the west by the Sea of Japan, while extending from the Sea of Okhotsk in the n ...

. File:Vukovar-watertower-after-war.jpg, Ruines du château d'eau de

Vukovar Vukovar () ( sr-Cyrl, Вуковар, hu, Vukovár, german: Wukowar) is a city in Croatia, in the eastern region of Slavonia. It contains Croatia's largest river port, located at the confluence of the Vuka and the Danube. Vukovar is the seat of ...

( Croatie).

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 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 language publications. ...

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. The main span is long, with the suspension cable ...

on the

East River The East River is a saltwater tidal estuary in New York City. The waterway, which is actually 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 the borough of Quee ...

, in

New York City New York, often called New York City or NYC, is the List of United States cities by population, most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the L ...

, 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 ( , ; es, link=no, Panamá ), officially the Republic of Panama ( es, República de Panamá), is a transcontinental country spanning the southern part of North America and the northern part of South America. It is bordered by Co ...

, 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'' (sometimes 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 and transportation o ...

" 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 is a large tidal estuary in the U.S. state of California, and gives its name to the San Francisco Bay Area. It is dominated by the big cities of San Francisco, San Jose, and Oakland. San Francisco Bay drains water f ...

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 ...

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