Gyrate bidiminished rhombicosidodecahedron

In geometry, the gyrate bidiminished rhombicosidodecahedron is one of the Johnson solids (J82).

Gyrate bidiminished rhombicosidodecahedron
TypeJohnson
J81J82J83
Faces10 triangles
20 squares
10 pentagons
2 decagons
Edges90
Vertices50
Vertex configuration10.2(4.5.10)
5x2(3.42.5)
4+8.2(3.4.5.4)
Symmetry groupCs
Dual polyhedron-
PropertiesConvex
Net

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]

It can be constructed as a rhombicosidodecahedron with two non-opposing pentagonal cupolae (J5) removed and a third is rotated 36 degrees. Related Johnson solids are:

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  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.