Augmented truncated cube

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Augmented truncated cube
Augmented truncated cube.png
Type Johnson
J65J66J67
Faces 3x4 triangles
1+4 squares
1+4 octagons
Edges 48
Vertices 28
Vertex configuration 2.4+8(3.82)
4(3.43)
8(3.4.3.8)
Symmetry group C4v
Dual polyhedron -
Properties convex
Net
Johnson solid 66 net.png

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 Johnson solid is one of 92 strictly convex polyhedra that is composed of regular polygon faces but are not uniform polyhedra (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]

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Augmented triangular prism 49th Johnson solid

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Biaugmented triangular prism 50th Johnson solid

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Augmented pentagonal prism 52nd Johnson solid

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Biaugmented pentagonal prism 53rd Johnson solid

In geometry, the biaugmented pentagonal prism is one of the Johnson solids. As the name suggests, it can be constructed by doubly augmenting a pentagonal prism by attaching square pyramids to two of its nonadjacent equatorial faces.

Augmented hexagonal prism 54th Johnson solid

In geometry, the augmented hexagonal prism is one of the Johnson solids. As the name suggests, it can be constructed by augmenting a hexagonal prism by attaching a square pyramid 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 55th Johnson solid

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Metabiaugmented hexagonal prism 56th Johnson solid

In geometry, the metabiaugmented hexagonal prism is one of the Johnson solids. As the name suggests, it can be constructed by doubly augmenting a hexagonal prism by attaching square pyramids to two of its nonadjacent, nonparallel equatorial faces. Attaching the pyramids to opposite equatorial faces yields a parabiaugmented hexagonal prism.

Triaugmented hexagonal prism 57th Johnson solid

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Augmented dodecahedron 58th Johnson solid

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Parabiaugmented dodecahedron 59th Johnson solid

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Triaugmented dodecahedron 61st Johnson solid

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Augmented truncated tetrahedron 65th Johnson solid

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Biaugmented truncated cube 67th Johnson solid

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Augmented truncated dodecahedron 68th Johnson solid

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Parabiaugmented truncated dodecahedron 69th Johnson solid

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Metabiaugmented truncated dodecahedron 70th Johnson solid

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Triaugmented truncated dodecahedron 71st Johnson solid

In geometry, the triaugmented truncated dodecahedron is one of the Johnson solids ; 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 onto three nonadjacent decagonal faces of a truncated dodecahedron.

References


  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 .