Metabidiminished rhombicosidodecahedron

Metabidiminished rhombicosidodecahedron
TypeJohnson
J80J81J82
Faces3x2+4 triangles
2+2+4x4 squares
3x2+4 pentagons
2 decagons
Edges90
Vertices50
Vertex configuration5×4(4.5.10)
3×2+6×4(3.4.5.4)
Symmetry groupC2v
Dual polyhedron-
PropertiesConvex
Net

In geometry, the metabidiminished rhombicosidodecahedron is one of the Johnson solids (J81).

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. Related Johnson solids are:

  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.