Editing Dome (section)

== Types ==
=== Beehive dome ===
{{see also|Beehive tomb}}
[[File:Atreus-2.jpg|thumb|Corbel dome]]

Also called a ''corbelled dome'',{{sfn|Höcker|2000|pp=181, 183}} ''cribbed dome'',{{sfn|Salvadori|1987|p=233}} or ''false dome'',{{sfn|Dror|2011|p=163}} these are different from a 'true dome' in that they consist of purely horizontal layers. As the layers get higher, each is slightly [[cantilever]]ed, or [[corbel]]ed, toward the center until meeting at the top. A monumental example is the Mycenaean [[Treasury of Atreus]] from the late [[Bronze Age]].{{sfn|Wright|2009|p=188}}

=== Braced dome ===
A single or double layer [[space frame]] in the form of a dome,{{sfn|Makowski|1962|p=62}} a ''braced dome'' is a generic term that includes ''ribbed'',{{sfn|Chen|Lui|2005|pp=24–18}} ''[[Johann Wilhelm Schwedler#Schwedler cupola|Schwedler]]'',{{sfn|Chen|Lui|2005|pp=24–18}} ''three-way grid'',{{sfn|Chen|Lui|2005|pp=24–18}} ''lamella'' or ''Kiewitt'',{{sfn|Chen|Lui|2005|pp=24–18, 24–19}} ''lattice'',{{sfn|Ramaswamy|Eekhout|2002|p=141}} and ''[[Geodesic dome|geodesic]] domes''.{{sfn|Chen|Lui|2005|pp=24–2, 24–18}} The different terms reflect different arrangements in the surface members. Braced domes often have a very low weight and are usually used to cover spans of up to 150 meters.{{sfn|Saka|2007|p=595}} Often prefabricated, their component members can either lie on the dome's surface of revolution, or be straight lengths with the connecting points or nodes lying upon the surface of revolution. Single-layer structures are called ''frame'' or ''skeleton'' types and double-layer structures are ''truss'' types, which are used for large spans. When the covering also forms part of the structural system, it is called a ''stressed skin'' type. The ''formed surface'' type consists of sheets joined at bent edges to form the structure.{{sfn|Makowski|1962|p=62}}

=== Cloister vault ===
{{Main|Cloister vault}}
[[File:Klostervalv.png|thumb|Domical or cloister vault]]

Also called ''domical vaults'' (a term sometimes also applied to sail vaults)<!-- this is an inconsistency in the sources, which is acknowledged by Dodge, 1984, page 273-->,{{sfn|Moffett|Fazio|Wodehouse|2003}}{{sfn|Dodge|1984|p=273}} ''polygonal domes'',{{sfn|Newman|Pevnser|1972|p=527}} ''coved domes'',{{sfn|Dien|2007|p=80}} ''gored domes'',{{sfn|Ward|1915|p=9}} ''segmental domes''{{sfn|Hourihane|2012|p=303}} (a term sometimes also used for saucer domes), ''paneled vaults'',{{sfn|Dodge|1984|p=268}} or ''pavilion vaults'',{{sfn|Sear|1983|p=79}} these are domes that maintain a polygonal shape in their horizontal cross section. The component curved surfaces of these vaults are called ''severies'', ''webs'', or ''cells''.{{sfn|Curl|2003|p=220}} The earliest known examples date to the first century BC, such as the [[Tabularium]] of Rome from 78 BC. Others include the Baths of Antoninus in [[Carthage]] (145–160) and the [[Palatine Chapel, Aachen|Palatine Chapel at Aachen]] (13th – 14th century).{{sfn|Como|2013|p=320}} The most famous example is the Renaissance octagonal dome of Filippo Brunelleschi over the Florence Cathedral. [[Thomas Jefferson]], the third president of the United States, installed an octagonal dome above the West front of his plantation house, [[Monticello]].{{sfn|Kern}}

=== Compound dome ===
[[File:Penditifkuppel.svg|thumb|Compound dome]]

Also called ''domes on pendentives''{{sfn|Karydis|2012|pp=362–363}} or ''pendentive domes''{{sfn|Hassan|Mazloomi|Omer|2010|p=105}} (a term also applied to sail vaults), compound domes have pendentives that support a smaller diameter dome immediately above them, as in the Hagia Sophia, or a drum and dome, as in many Renaissance and post-Renaissance domes, with both forms resulting in greater height.{{sfn|Catholic}}

=== Crossed-arch dome ===
[[File:Cordoba Mosque 13.jpg|thumb|Crossed-arch dome (Cordoba Mosque)]]

One of the earliest types of ribbed vault, the first known examples are found in the [[Mosque–Cathedral of Córdoba|Great Mosque of Córdoba]] in the 10th century. Rather than meeting in the center of the dome, the ribs characteristically intersect one another off-center, forming an empty polygonal space in the center. Geometry is a key element of the designs, with the octagon being perhaps the most popular shape used. Whether the arches are structural or purely decorative remains a matter of debate. The type may have an eastern origin, although the issue is also unsettled. Examples are found in Spain, North Africa, Armenia, Iran, France, and Italy.{{sfn|Fuentes|Huerta|2010|pp=346–352}}

=== Ellipsoidal dome ===
{{Main|Ellipsoidal dome}}

The ellipsoidal dome is a surface formed by the rotation around a vertical axis of a [[Ellipse|semi-ellipse]]. Like other "rotational domes" formed by the rotation of a curve around a vertical axis, ellipsoidal domes have circular bases and horizontal sections and are a type of "circular dome" for that reason.{{sfn|Arun|2006|p=304}}

=== Geodesic dome ===
{{Main|Geodesic dome}}
[[File:Biosphere montreal.JPG|thumb|Geodesic dome ([[Montreal Biosphere]], Canada)]]

''Geodesic domes'' are the upper portion of geodesic spheres. They are composed of a framework of triangles in a [[polyhedron]] pattern.{{sfn|Langmead|Garnaut|2001|p=131}} The structures are named for [[geodesic]]s and are based upon geometric shapes such as [[icosahedron]]s, [[octahedron]]s or [[tetrahedron]]s.{{sfn|Langmead|Garnaut|2001|p=131}}{{sfn|Hourihane|2012|p=302}} Such domes can be created using a limited number of simple elements and joints and efficiently resolve a dome's internal forces. Their efficiency is said to increase with size.{{sfn|Ambrose|Tripeny|2011|p=36}} Although not first invented by [[Buckminster Fuller]], they are associated with him because he designed many geodesic domes and patented them in the United States.{{sfn|Denny|2010|p=140}}

=== Hemispherical dome ===
[[File:Kupolvalv.svg|thumb|Hemispherical dome]]

The ''hemispherical dome'' is a surface formed by the rotation around a vertical axis of a [[semicircle]]. Like other "rotational domes" formed by the rotation of a curve around a vertical axis, hemispherical domes have circular bases and horizontal sections and are a type of "circular dome" for that reason. They experience vertical compression along their meridians, but horizontally experience compression only in the portion above 51.8 degrees from the top. Below this point, hemispherical domes experience tension horizontally, and usually require buttressing to counteract it.{{sfn|Arun|2006|p=304}} According to E. Baldwin Smith, it was a shape likely known to the Assyrians, defined by Greek theoretical mathematicians, and standardized by Roman builders.{{sfn|Smith|1950|pp=8, 9}}

=== Onion dome ===
{{Main|Onion dome}}

''Bulbous domes'' bulge out beyond their base diameters, offering a profile greater than a hemisphere.{{sfn|Hourihane|2012|p=302}} An ''onion dome'' is a greater than hemispherical dome with a pointed top in an [[ogee]] profile.{{sfn|Hourihane|2012|p=302}} They are found in the [[Near East]], [[Middle East]], Persia, and India and may not have had a single point of origin. Their appearance in northern Russian architecture predates the [[Mongol invasion of Rus'#The age of Tatar rule|Tatar occupation of Russia]] and so is not easily explained as the result of that influence.{{sfn|Hamilton|1983|p=42}} They became popular in the second half of the 15th century in the [[Low Countries]] of Northern Europe, possibly inspired by the finials of [[minaret]]s in Egypt and Syria, and developed in the 16th and 17th centuries in the Netherlands before spreading to Germany, becoming a popular element of the baroque architecture of Central Europe. German bulbous domes were also influenced by Russian and Eastern European domes.{{sfn|Born|1944|pp=220–221}} The examples found in various European architectural styles are typically wooden.{{sfn|Hourihane|2012|p=302}} Examples include Kazan Church in [[Kolomenskoye]] and the [[Royal Pavilion|Brighton Pavilion]] by [[John Nash (architect)|John Nash]].{{sfn|Hourihane|2012|p=302}} In Islamic architecture, they are typically made of masonry, rather than timber, with the thick and heavy bulging portion serving to buttress against the tendency of masonry domes to spread at their bases. The Taj Mahal is a famous example.{{sfn|Hourihane|2012|p=302}}

=== Oval dome ===
{{see also|Elliptical dome}}
[[File:Benfoto-Roma2013-286.jpg|thumb|An oval dome (Rome, Italy)]]

An ''oval dome'' is a dome of [[oval]] shape in plan, profile, or both. The term comes from the Latin ''ovum'', meaning "egg". The earliest oval domes were used by convenience in corbelled stone huts as rounded but geometrically undefined coverings, and the first examples in Asia Minor date to around 4000 B.C. The geometry was eventually defined using combinations of circular arcs, transitioning at points of tangency. If the Romans created oval domes, it was only in exceptional circumstances. The Roman foundations of the oval plan [[St. Gereon's Basilica, Cologne|Church of St. Gereon in Cologne]] point to a possible example. Domes in the Middle Ages also tended to be circular, though the church of [[Santo Tomás de las Ollas]] in Spain has an oval dome over its oval plan. Other examples of medieval oval domes can be found covering rectangular bays in churches. Oval plan churches became a type in the [[Renaissance]] and popular in the [[Baroque]] style.{{sfn|Huerta|2007|p=231}} The dome built for the basilica of [[Vicoforte]] by Francesco Gallo was one of the largest and most complex ever made.{{sfn|Bagliani|2009}} Although the ellipse was known, in practice, domes of this shape were created by combining segments of circles. Popular in the 16th and 17th centuries, oval and elliptical plan domes can vary their dimensions in three axes or two axes. {{citation needed|date=December 2019}} A sub-type with the long axis having a semicircular section is called a Murcia dome, as in the Chapel of the Junterones at [[Murcia Cathedral]]. When the short axis has a semicircular section, it is called a Melon dome.{{citation needed|date=December 2019}}

=== Paraboloid dome ===
A [[paraboloid]] dome is a surface formed by the rotation around a vertical axis of a sector of a parabola. Like other "rotational domes" formed by the rotation of a curve around a vertical axis, paraboloid domes have circular bases and horizontal sections and are a type of "circular dome" for that reason. Because of their shape, paraboloid domes experience only compression, both radially and horizontally.{{sfn|Arun|2006|p=304}}

=== Sail dome ===
[[File:Haengekuppel.png|thumb|Sail dome]]

Also called ''sail vaults'',{{sfn|Fleming|Honour|Pevsner|1991|pp=127, 463}} ''handkerchief vaults'',{{sfn|Fleming|Honour|Pevsner|1991|p=462}} ''domical vaults'' (a term sometimes also applied to cloister vaults)<!-- this is an inconsistency in the sources, which is acknowledged by Dodge, 1984, page 273-->,{{sfn|Dodge|1984|p=273}} ''pendentive domes''{{sfn|Dodge|1984|p=274}}{{sfn|Bellini|2017|p=1}} (a term that has also been applied to compound domes), ''Bohemian vaults'',{{sfn|Burckhardt|1987|p=58}} or ''Byzantine domes'',{{citation needed|date=February 2023}} this type can be thought of as [[pendentives]] that, rather than merely touching each other to form a circular base for a drum or compound dome, smoothly continue their curvature to form the dome itself. The dome gives the impression of a square sail pinned down at each corner and billowing upward.{{sfn|Fleming|Honour|Pevsner|1991|p=127}} These can also be thought of as saucer domes upon pendentives.{{sfn|Hourihane|2012|p=303}} Sail domes are based upon the shape of a hemisphere and are not to be confused with [[Paraboloid#Elliptic paraboloid|elliptic parabolic]] vaults, which appear similar but have different characteristics.{{sfn|Arun|2006|p=304}} In addition to semicircular sail vaults there are variations in geometry such as a low rise to span ratio or covering a rectangular plan. Sail vaults of all types have a variety of thrust conditions along their borders, which can cause problems, but have been widely used from at least the sixteenth century. The second floor of the [[Llotja de la Seda]] is covered by a series of nine meter wide sail vaults.{{citation needed|date=February 2023}}

=== Saucer dome ===
[[File:Louisiana superdome 2004.jpg|thumb|Saucer dome ([[Louisiana Superdome]], Louisiana, US)]]

Also called ''segmental domes''{{sfn|Dodge|1984|p=263}} (a term sometimes also used for cloister vaults), or ''calottes'',{{sfn|Fleming|Honour|Pevsner|1991|p=127}} these have profiles of [[Circular segment|less than half a circle]]. Because they reduce the portion of the dome in tension, these domes are strong but have increased radial thrust.{{sfn|Dodge|1984|p=263}} Many of the largest existing domes are of this shape.

Masonry saucer domes, because they exist entirely in compression, can be built much thinner than other dome shapes without becoming unstable. The trade-off between the proportionately increased horizontal thrust at their abutments and their decreased weight and quantity of materials may make them more economical, but they are more vulnerable to damage from movement in their supports.{{sfn|Gye|1988|pp=142–143}}

=== Umbrella dome ===
[[File:Chiesa di santa croce, cappella dei pazzi, cupola 1.JPG|thumb|Umbrella dome ([[Santa Croce, Florence]])]]

Also called ''gadrooned'',{{sfn|Yaghan|2003|p=69}} ''fluted'',{{sfn|Yaghan|2003|p=69}} ''organ-piped'',{{sfn|Yaghan|2003|p=69}} ''pumpkin'',{{sfn|Fleming|Honour|Pevsner|1991|p=127}} ''melon'',{{sfn|Fleming|Honour|Pevsner|1991|p=127}} ''ribbed'',{{sfn|Yaghan|2003|p=69}} ''parachute'',{{sfn|Fleming|Honour|Pevsner|1991|p=127}} ''scalloped'',{{sfn|Krautheimer|1980|pp=121, 132}} or ''lobed'' domes,{{sfn|Ward|1915|pp=116–117}} these are a type of dome divided at the base into curved segments, which follow the curve of the [[Multiview orthographic projection#Elevation|elevation]].{{sfn|Fleming|Honour|Pevsner|1991|p=127}} "Fluted" may refer specifically to this pattern as an external feature, such as was common in [[Mamluk architecture|Mamluk Egypt]].{{sfn|Hourihane|2012|p=302}} The "ribs" of a dome are the radial lines of masonry that extend from the crown down to the springing.{{sfn|Dumser|2010|p=436}} The central dome of the [[Hagia Sophia]] uses the ribbed method, which accommodates a ring of windows between the ribs at the base of the dome. The central dome of [[St. Peter's Basilica]] also uses this method.