Augmented truncated dodecahedron

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Augmented truncated dodecahedron
Augmented truncated dodecahedron.png
Type Johnson
J67J68J69
Faces 5x5 triangles
5 squares
1 pentagon
1+2x5 decagons
Edges 105
Vertices 65
Vertex configuration 4.5+3.10(3.102)
5(3.4.5.4)
10(3.4.3.10)
Symmetry group C5v
Dual polyhedron -
Properties convex
Net
Johnson solid 68 net.png

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.

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]

  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 .

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Augmented pentagonal prism 52nd Johnson solid

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Biaugmented pentagonal prism 53rd Johnson solid

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Augmented hexagonal prism 54th Johnson solid

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Parabiaugmented dodecahedron 59th Johnson solid

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Triaugmented dodecahedron 61st Johnson solid

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Biaugmented truncated cube 67th Johnson solid

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