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- Johnson solids

Elongated pentagonal orthobicupola

In geometry, the elongated pentagonal orthobicupola or cantellated pentagonal prism is one of the Johnson solids (J38). As the name suggests, it can be constructed by elongating a pentagonal orthobicu

Elongated triangular pyramid

In geometry, the elongated triangular pyramid is one of the Johnson solids (J7). As the name suggests, it can be constructed by elongating a tetrahedron by attaching a triangular prism to its base. Li

List of Johnson solids

In geometry, a Johnson solid is a strictly convex polyhedron, each face of which is a regular polygon, but which is not uniform, i.e., not a Platonic solid, Archimedean solid, prism or antiprism. In 1

Metabiaugmented truncated dodecahedron

In geometry, the metabiaugmented truncated dodecahedron is one of the Johnson solids (J70). As its name suggests, it is created by attaching two pentagonal cupolas (J5) onto two nonadjacent, nonparall

Augmented tridiminished icosahedron

In geometry, the augmented tridiminished icosahedron is one of theJohnson solids (J64). It can be obtained by joining a tetrahedron to another Johnson solid, the tridiminished icosahedron (J63). A Joh

Elongated triangular gyrobicupola

In geometry, the elongated triangular gyrobicupola is one of the Johnson solids (J36). As the name suggests, it can be constructed by elongating a "triangular gyrobicupola," or cuboctahedron, by inser

Diminished rhombicosidodecahedron

In geometry, the diminished rhombicosidodecahedron is one of the Johnson solids (J76). It can be constructed as a rhombicosidodecahedron with one pentagonal cupola removed. A Johnson solid is one of 9

Elongated triangular orthobicupola

In geometry, the elongated triangular orthobicupola or cantellated triangular prism is one of the Johnson solids (J35). As the name suggests, it can be constructed by elongating a triangular orthobicu

Square gyrobicupola

In geometry, the square gyrobicupola is one of the Johnson solids (J29). Like the square orthobicupola (J28), it can be obtained by joining two square cupolae (J4) along their bases. The difference is

Cupola (geometry)

In geometry, a cupola is a solid formed by joining two polygons, one (the base) with twice as many edges as the other, by an alternating band of isosceles triangles and rectangles. If the triangles ar

Gyroelongated square pyramid

In geometry, the gyroelongated square pyramid is one of the Johnson solids (J10). As its name suggests, it can be constructed by taking a square pyramid and "gyroelongating" it, which in this case inv

Bigyrate diminished rhombicosidodecahedron

In geometry, the bigyrate diminished rhombicosidodecahedron is one of the Johnson solids (J79). It can be constructed as a rhombicosidodecahedron with two pentagonal cupolae rotated through 36 degrees

Triaugmented truncated dodecahedron

In geometry, the triaugmented truncated dodecahedron is one of the Johnson solids (J71); of them, it has the greatest volume in proportion to the cube of the side length. As its name suggests, it is c

Biaugmented truncated cube

In geometry, the biaugmented truncated cube is one of the Johnson solids (J67). As its name suggests, it is created by attaching two square cupolas (J4) onto two parallel octagonal faces of a truncate

Pentagonal gyrocupolarotunda

In geometry, the pentagonal gyrocupolarotunda is one of the Johnson solids (J33). Like the pentagonal orthocupolarotunda (J32), it can be constructed by joining a pentagonal cupola (J5) and a pentagon

Pentagonal gyrobicupola

In geometry, the pentagonal gyrobicupola is one of the Johnson solids (J31). Like the pentagonal orthobicupola (J30), it can be obtained by joining two pentagonal cupolae (J5) along their bases. The d

Parabiaugmented truncated dodecahedron

In geometry, the parabiaugmented truncated dodecahedron is one of the Johnson solids (J69). As its name suggests, it is created by attaching two pentagonal cupolas (J5) onto two parallel decagonal fac

Gyroelongated triangular cupola

In geometry, the gyroelongated triangular cupola is one of the Johnson solids (J22). It can be constructed by attaching a hexagonal antiprism to the base of a triangular cupola (J3). This is called "g

Sphenocorona

In geometry, the sphenocorona is one of the Johnson solids (J86). It is one of the elementary Johnson solids that do not arise from "cut and paste" manipulations of the Platonic and Archimedean solids

Metabigyrate rhombicosidodecahedron

In geometry, the metabigyrate rhombicosidodecahedron is one of the Johnson solids (J74). It can be constructed as a rhombicosidodecahedron with two non-opposing pentagonal cupolae rotated through 36 d

Metabiaugmented dodecahedron

In geometry, the metabiaugmented dodecahedron is one of the Johnson solids (J60). It can be viewed as a dodecahedron with two pentagonal pyramids (J2) attached to two faces that are separated by one f

Pentagonal cupola

In geometry, the pentagonal cupola is one of the Johnson solids (J5). It can be obtained as a slice of the rhombicosidodecahedron. The pentagonal cupola consists of 5 equilateral triangles, 5 squares,

Pentagonal orthobirotunda

In geometry, the pentagonal orthobirotunda is one of the Johnson solids (J34). It can be constructed by joining two pentagonal rotundae (J6) along their decagonal faces, matching like faces. A Johnson

Triangular orthobicupola

In geometry, the triangular orthobicupola is one of the Johnson solids (J27). As the name suggests, it can be constructed by attaching two triangular cupolas (J3) along their bases. It has an equal nu

Birotunda

In geometry, a birotunda is any member of a family of dihedral-symmetric polyhedra, formed from two rotunda adjoined through the largest face. They are similar to a bicupola but instead of alternating

Elongated square gyrobicupola

In geometry, the elongated square gyrobicupola or pseudo-rhombicuboctahedron is one of the Johnson solids (J37). It is not usually considered to be an Archimedean solid, even though its faces consist

Biaugmented pentagonal prism

In geometry, the biaugmented pentagonal prism is one of the Johnson solids (J53). As the name suggests, it can be constructed by doubly augmenting a pentagonal prism by attaching square pyramids (J1)

Tridiminished rhombicosidodecahedron

In geometry, the tridiminished rhombicosidodecahedron is one of the Johnson solids (J83). It can be constructed as a rhombicosidodecahedron with three pentagonal cupolae removed. A Johnson solid is on

Gyroelongated triangular bicupola

In geometry, the gyroelongated triangular bicupola is one of the Johnson solids (J44). As the name suggests, it can be constructed by gyroelongating a triangular bicupola (either triangular orthobicup

Gyroelongated pentagonal cupolarotunda

In geometry, the gyroelongated pentagonal cupolarotunda is one of the Johnson solids (J47). As the name suggests, it can be constructed by gyroelongating a pentagonal cupolarotunda (J32 or J33) by ins

Triangular cupola

In geometry, the triangular cupola is one of the Johnson solids (J3). It can be seen as half a cuboctahedron. A Johnson solid is one of 92 strictly convex polyhedra that is composed of regular polygon

Gyroelongated pentagonal cupola

In geometry, the gyroelongated pentagonal cupola is one of the Johnson solids (J24). As the name suggests, it can be constructed by gyroelongating a pentagonal cupola (J5) by attaching a decagonal ant

Paragyrate diminished rhombicosidodecahedron

In geometry, the paragyrate diminished rhombicosidodecahedron is one of the Johnson solids (J77). It can be constructed as a rhombicosidodecahedron with one pentagonal cupola rotated through 36 degree

Snub square antiprism

In geometry, the snub square antiprism is one of the Johnson solids (J85).A Johnson solid is one of 92 strictly convex polyhedra that is composed of regular polygon faces but are not uniform polyhedra

Gyroelongated pentagonal rotunda

In geometry, the gyroelongated pentagonal rotunda is one of the Johnson solids (J25). As the name suggests, it can be constructed by gyroelongating a pentagonal rotunda (J6) by attaching a decagonal a

Augmented truncated dodecahedron

In geometry, the augmented truncated dodecahedron is one of the Johnson solids (J68). As its name suggests, it is created by attaching a pentagonal cupola (J5) onto one decagonal face of a truncated d

Elongated pentagonal cupola

In geometry, the elongated pentagonal cupola is one of the Johnson solids (J20). As the name suggests, it can be constructed by elongating a pentagonal cupola (J5) by attaching a decagonal prism to it

Elongated pentagonal gyrobirotunda

In geometry, the elongated pentagonal gyrobirotunda is one of the Johnson solids (J43). As the name suggests, it can be constructed by elongating a "pentagonal gyrobirotunda," or icosidodecahedron (on

Gyrate rhombicosidodecahedron

In geometry, the gyrate rhombicosidodecahedron is one of the Johnson solids (J72). It is also a canonical polyhedron. A Johnson solid is one of 92 strictly convex polyhedra that is composed of regular

Sphenomegacorona

In geometry, the sphenomegacorona is one of the Johnson solids (J88). It is one of the elementary Johnson solids that do not arise from "cut and paste" manipulations of the Platonic and Archimedean so

Elongated pentagonal orthobirotunda

In geometry, the elongated pentagonal orthobirotunda is one of the Johnson solids (J42). Its Conway polyhedron notation is at5jP5. As the name suggests, it can be constructed by elongating a pentagona

Elongated pentagonal pyramid

In geometry, the elongated pentagonal pyramid is one of the Johnson solids (J9). As the name suggests, it can be constructed by elongating a pentagonal pyramid (J2) by attaching a pentagonal prism to

Elongated pentagonal gyrobicupola

In geometry, the elongated pentagonal gyrobicupola is one of the Johnson solids (J39). As the name suggests, it can be constructed by elongating a pentagonal gyrobicupola (J31) by inserting a decagona

Pentagonal pyramid

In geometry, a pentagonal pyramid is a pyramid with a pentagonal base upon which are erected five triangular faces that meet at a point (the apex). Like any pyramid, it is self-dual. The regular penta

Augmented triangular prism

In geometry, the augmented triangular prism is one of the Johnson solids (J49). As the name suggests, it can be constructed by augmenting a triangular prism by attaching a square pyramid (J1) to one o

Augmented truncated cube

In geometry, the augmented truncated cube is one of the Johnson solids (J66). As its name suggests, it is created by attaching a square cupola (J4) onto one octagonal face of a truncated cube. A Johns

Elongated square cupola

In geometry, the elongated square cupola is one of the Johnson solids (J19). As the name suggests, it can be constructed by elongating a square cupola (J4) by attaching an octagonal prism to its base.

Triaugmented hexagonal prism

In geometry, the triaugmented hexagonal prism is one of the Johnson solids (J57). As the name suggests, it can be constructed by triply augmenting a hexagonal prism by attaching square pyramids (J1) t

Square cupola

In geometry, the square cupola, sometimes called lesser dome, is one of the Johnson solids (J4). It can be obtained as a slice of the rhombicuboctahedron. As in all cupolae, the base polygon has twice

Metabiaugmented hexagonal prism

In geometry, the metabiaugmented hexagonal prism is one of the Johnson solids (J56). As the name suggests, it can be constructed by doubly augmenting a hexagonal prism by attaching square pyramids (J1

Parabigyrate rhombicosidodecahedron

In geometry, the parabigyrate rhombicosidodecahedron is one of the Johnson solids (J73). It can be constructed as a rhombicosidodecahedron with two opposing pentagonal cupolae rotated through 36 degre

Elongated pentagonal orthocupolarotunda

In geometry, the elongated pentagonal orthocupolarotunda is one of the Johnson solids (J40). As the name suggests, it can be constructed by elongating a pentagonal orthocupolarotunda (J32) by insertin

Metabidiminished icosahedron

In geometry, the metabidiminished icosahedron is one of the Johnson solids (J62). The name refers to one way of constructing it, by removing two pentagonal pyramids (J2) from a regular icosahedron, re

Johnson solid

In geometry, a Johnson solid is a strictly convex polyhedron each face of which is a regular polygon. There is no requirement that each face must be the same polygon, or that the same polygons join ar

Augmented pentagonal prism

In geometry, the augmented pentagonal prism is one of the Johnson solids (J52). As the name suggests, it can be constructed by augmenting a pentagonal prism by attaching a square pyramid (J1) to one o

Gyroelongated pentagonal pyramid

In geometry, the gyroelongated pentagonal pyramid is one of the Johnson solids (J11). As its name suggests, it is formed by taking a pentagonal pyramid and "gyroelongating" it, which in this case invo

Elongated square bipyramid

In geometry, the elongated square bipyramid (or elongated octahedron) is one of the Johnson solids (J15). As the name suggests, it can be constructed by elongating an octahedron by inserting a cube be

Disphenocingulum

In geometry, the disphenocingulum or pentakis elongated gyrobifastigium is one of the Johnson solids (J90). It is one of the elementary Johnson solids that do not arise from "cut and paste" manipulati

Snub disphenoid

In geometry, the snub disphenoid, Siamese dodecahedron, triangular dodecahedron, trigonal dodecahedron, or dodecadeltahedron is a convex polyhedron with twelve equilateral triangles as its faces. It i

Pentagonal orthobicupola

In geometry, the pentagonal orthobicupola is one of the Johnson solids (J30). As the name suggests, it can be constructed by joining two pentagonal cupolae (J5) along their decagonal bases, matching l

Augmented sphenocorona

In geometry, the augmented sphenocorona is one of the Johnson solids (J87), and is obtained by adding a square pyramid to one of the square faces of the sphenocorona. It is the only Johnson solid aris

Metagyrate diminished rhombicosidodecahedron

In geometry, the metagyrate diminished rhombicosidodecahedron is one of the Johnson solids (J78). It can be constructed as a rhombicosidodecahedron with one pentagonal cupola (J5) rotated through 36 d

Elongated triangular bipyramid

In geometry, the elongated triangular bipyramid (or dipyramid) or triakis triangular prism is one of the Johnson solids (J14), convex polyhedra whose faces are regular polygons. As the name suggests,

Elongated pentagonal bipyramid

In geometry, the elongated pentagonal bipyramid or pentakis pentagonal prism is one of the Johnson solids (J16). As the name suggests, it can be constructed by elongating a pentagonal bipyramid (J13)

Gyroelongated square bicupola

In geometry, the gyroelongated square bicupola is one of the Johnson solids (J45). As the name suggests, it can be constructed by gyroelongating a square bicupola (J28 or J29) by inserting an octagona

Augmented truncated tetrahedron

In geometry, the augmented truncated tetrahedron is one of the Johnson solids (J65). It is created by attaching a triangular cupola (J3) to one hexagonal face of a truncated tetrahedron. A Johnson sol

Elongated triangular cupola

In geometry, the elongated triangular cupola is one of the Johnson solids (J18). As the name suggests, it can be constructed by elongating a triangular cupola (J3) by attaching a hexagonal prism to it

Gyrobifastigium

In geometry, the gyrobifastigium is the 26th Johnson solid (J26). It can be constructed by joining two face-regular triangular prisms along corresponding square faces, giving a quarter-turn to one pri

Metabidiminished rhombicosidodecahedron

In geometry, the metabidiminished rhombicosidodecahedron is one of the Johnson solids (J81). A Johnson solid is one of 92 strictly convex polyhedra that is composed of regular polygon faces but are no

Augmented hexagonal prism

In geometry, the augmented hexagonal prism is one of the Johnson solids (J54). As the name suggests, it can be constructed by augmenting a hexagonal prism by attaching a square pyramid (J1) to one of

Parabiaugmented dodecahedron

In geometry, the parabiaugmented dodecahedron is one of the Johnson solids (J59). It can be seen as a dodecahedron with two pentagonal pyramids (J2) attached to opposite faces. When pyramids are attac

Hebesphenomegacorona

In geometry, the hebesphenomegacorona is one of the Johnson solids (J89). It is one of the elementary Johnson solids that do not arise from "cut and paste" manipulations of the Platonic and Archimedea

Gyroelongated square bipyramid

In geometry, the gyroelongated square bipyramid, heccaidecadeltahedron, or tetrakis square antiprism is one of the Johnson solids (J17). As the name suggests, it can be constructed by gyroelongating a

Parabidiminished rhombicosidodecahedron

In geometry, the parabidiminished rhombicosidodecahedron is one of the Johnson solids (J80). It is also a canonical polyhedron. A Johnson solid is one of 92 strictly convex polyhedra that is composed

Pentagonal orthocupolarotunda

In geometry, the pentagonal orthocupolarotunda is one of the Johnson solids (J32). As the name suggests, it can be constructed by joining a pentagonal cupola (J5) and a pentagonal rotunda (J6) along t

Gyrate bidiminished rhombicosidodecahedron

In geometry, the gyrate bidiminished rhombicosidodecahedron is one of the Johnson solids (J82). A Johnson solid is one of 92 strictly convex polyhedra that is composed of regular polygon faces but are

Square pyramid

In geometry, a square pyramid is a pyramid having a square base. If the apex is perpendicularly above the center of the square, it is a right square pyramid, and has C4v symmetry. If all edge lengths

Rotunda (geometry)

In geometry, a rotunda is any member of a family of dihedral-symmetric polyhedra. They are similar to a cupola but instead of alternating squares and triangles, it alternates pentagons and triangles a

Triangular bipyramid

In geometry, the triangular bipyramid (or dipyramid) is a type of hexahedron, being the first in the infinite set of face-transitive bipyramids. It is the dual of the triangular prism with 6 isosceles

Triaugmented dodecahedron

In geometry, the triaugmented dodecahedron is one of the Johnson solids (J61). It can be seen as a dodecahedron with three pentagonal pyramids (J2) attached to nonadjacent faces. When pyramids are att

Gyroelongated pentagonal bicupola

In geometry, the gyroelongated pentagonal bicupola is one of the Johnson solids (J46). As the name suggests, it can be constructed by gyroelongating a pentagonal bicupola (J30 or J31) by inserting a d

Trigyrate rhombicosidodecahedron

In geometry, the trigyrate rhombicosidodecahedron is one of the Johnson solids (J75). It contains 20 triangles, 30 squares and 12 pentagons. It is also a canonical polyhedron. A Johnson solid is one o

Bilunabirotunda

In geometry, the bilunabirotunda is one of the Johnson solids (J91). A Johnson solid is one of 92 strictly convex polyhedra that is composed of regular polygon faces but are not uniform polyhedra (tha

Gyroelongated pentagonal birotunda

In geometry, the gyroelongated pentagonal birotunda is one of the Johnson solids (J48). As the name suggests, it can be constructed by gyroelongating a pentagonal birotunda (either J34 or the icosidod

Gyroelongated square cupola

In geometry, the gyroelongated square cupola is one of the Johnson solids (J23). As the name suggests, it can be constructed by gyroelongating a square cupola (J4) by attaching an octagonal antiprism

Biaugmented triangular prism

In geometry, the biaugmented triangular prism is one of the Johnson solids (J50). As the name suggests, it can be constructed by augmenting a triangular prism by attaching square pyramids (J1) to two

Pentagonal bipyramid

In geometry, the pentagonal bipyramid (or dipyramid) is third of the infinite set of face-transitive bipyramids, and the 13th Johnson solid (J13). Each bipyramid is the dual of a uniform prism. Althou

Triaugmented triangular prism

In geometry, the triaugmented triangular prism is a convex polyhedron with 14 equilateral triangles as its faces. It can be constructed from a triangular prism by attaching equilateral square pyramids

Square orthobicupola

In geometry, the square orthobicupola is one of the Johnson solids (J28). As the name suggests, it can be constructed by joining two square cupolae (J4) along their octagonal bases, matching like face

Elongated pentagonal rotunda

In geometry, the elongated pentagonal rotunda is one of the Johnson solids (J21). As the name suggests, it can be constructed by elongating a pentagonal rotunda (J6) by attaching a decagonal prism to

Augmented dodecahedron

In geometry, the augmented dodecahedron is one of the Johnson solids (J58), consisting of a dodecahedron with a pentagonal pyramid (J2) attached to one of the faces. When two or three such pyramids ar

Parabiaugmented hexagonal prism

In geometry, the parabiaugmented hexagonal prism is one of the Johnson solids (J55). As the name suggests, it can be constructed by doubly augmenting a hexagonal prism by attaching square pyramids (J1

Tridiminished icosahedron

In geometry, the tridiminished icosahedron is one of the Johnson solids (J63). The name refers to one way of constructing it, by removing three pentagonal pyramids (J2) from a regular icosahedron, whi

Elongated pentagonal gyrocupolarotunda

In geometry, the elongated pentagonal gyrocupolarotunda is one of the Johnson solids (J41). As the name suggests, it can be constructed by elongating a pentagonal gyrocupolarotunda (J33) by inserting

Elongated square pyramid

In geometry, the elongated square pyramid is one of the Johnson solids (J8). As the name suggests, it can be constructed by elongating a square pyramid (J1) by attaching a cube to its square base. Lik

Triangular hebesphenorotunda

In geometry, the triangular hebesphenorotunda is one of the Johnson solids (J92). A Johnson solid is one of 92 strictly convex polyhedra that is composed of regular polygon faces but are not uniform p

Pentagonal rotunda

In geometry, the pentagonal rotunda is one of the Johnson solids (J6). It can be seen as half of an icosidodecahedron, or as half of a pentagonal orthobirotunda. It has a total of 17 faces. A Johnson

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