Triaugmented truncated dodecahedron

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Triaugmented truncated dodecahedron
Triaugmented truncated dodecahedron.png
Type Johnson
J70 – J71 – J72
Faces 2+3x3+4x6 triangles
3+2x6 squares
3 pentagons
3x3 decagons
Edges 135
Vertices 75
Vertex configuration 4x3+3x6(3.102)
3+2x6(3.4.5.4)
5x6(3.4.3.10)
Symmetry group C3v
Dual polyhedron -
Properties convex
Net
Johnson solid 71 net.png

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.

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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