Metabiaugmented dodecahedron

Last updated • 1 min readFrom Wikipedia, The Free Encyclopedia
Metabiaugmented dodecahedron
Metabiaugmented dodecahedron.png
Type Johnson
J59 - J60 - J61
Faces 2+2.4 triangles
3.2+4 pentagons
Edges 40
Vertices 22
Vertex configuration 3.2+4(53)
2+2.4(32.52)
2(35)
Symmetry group C2v
Dual polyhedron -
Properties convex
Net
Johnson solid 60 net.png

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 face. (The two faces are not opposite, but not adjacent either.) When pyramids are attached to a dodecahedron in other ways, they may result in an augmented dodecahedron, a parabiaugmented dodecahedron, a triaugmented dodecahedron, or even a pentakis dodecahedron if the faces are made to be irregular.

A Johnson solid is one of 92 strictly convex polyhedra that have regular faces but are not uniform (that is, they are not Platonic solids, Archimedean solids, prisms, or antiprisms). They were named by Norman Johnson, who first listed these polyhedra in 1966. [1]

  1. ↑ Johnson, Norman W. (1966), "Convex polyhedra with regular faces", Canadian Journal of Mathematics , 18: 169–200, doi:10.4153/cjm-1966-021-8, MR   0185507, Zbl   0132.14603 .
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.

Related Research Articles

Triaugmented triangular prism Johnson solid

In geometry, the triaugmented triangular prism or tetracaidecadeltahedron is one of the Johnson solids (J51). As the name suggests, it can be constructed by attaching square pyramids (J1) to each of the three equatorial faces of the triangular prism. It is a deltahedron.

Elongated pentagonal pyramid Johnson solid

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 its base.

Elongated square pyramid Johnson solid

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. Like any elongated pyramid, it is topologically self-dual.

Augmented triangular prism Johnson solid

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 of its equatorial faces. The resulting solid bears a superficial resemblance to the gyrobifastigium (J26), the difference being that the latter is constructed by attaching a second triangular prism, rather than a square pyramid.

Biaugmented triangular prism Johnson solid

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 of its equatorial faces.

Augmented pentagonal prism Johnson solid

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 of its equatorial faces.

Biaugmented pentagonal prism Johnson solid

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) to two of its nonadjacent equatorial faces.

Augmented hexagonal prism Johnson solid

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 its equatorial faces. When two or three such pyramids are attached, the result may be a parabiaugmented hexagonal prism, a metabiaugmented hexagonal prism or a triaugmented hexagonal prism.

Parabiaugmented hexagonal prism Johnson solid

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) to two of its nonadjacent, parallel (opposite) equatorial faces. Attaching the pyramids to nonadjacent, nonparallel equatorial faces yields a metabiaugmented hexagonal prism.

Metabiaugmented hexagonal prism Johnson solid

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) to two of its nonadjacent, nonparallel equatorial faces. Attaching the pyramids to opposite equatorial faces yields a parabiaugmented hexagonal prism.

Triaugmented hexagonal prism Johnson solid

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) to three of its nonadjacent equatorial faces.

Augmented dodecahedron Johnson solid

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 are attached, the result may be a parabiaugmented dodecahedron, a metabiaugmented dodecahedron or a triaugmented dodecahedron.

Parabiaugmented dodecahedron Johnson solid

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 attached to a dodecahedron in other ways, they may result in an augmented dodecahedron, a metabiaugmented dodecahedron, a triaugmented dodecahedron, or even a pentakis dodecahedron if the faces are made to be irregular.

Triaugmented dodecahedron Johnson solid

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.

Triangular orthobicupola Johnson solid

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 number of squares and triangles at each vertex; however, it is not vertex-transitive. It is also called an anticuboctahedron, twisted cuboctahedron or disheptahedron.

Augmented truncated dodecahedron Johnson solid

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 dodecahedron.

Parabiaugmented truncated dodecahedron Johnson solid

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 faces of a truncated dodecahedron.

Metabiaugmented truncated dodecahedron Johnson solid

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, nonparallel decagonal faces of a truncated dodecahedron.

Triaugmented truncated dodecahedron Johnson solid

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 created by attaching three pentagonal cupolas (J5) onto three nonadjacent decagonal faces of a truncated dodecahedron.

Bicupola (geometry) solid formed by connecting two cupolae on their bases

In geometry, a bicupola is a solid formed by connecting two cupolae on their bases.