Parabidiminished rhombicosidodecahedron

In geometry, the parabidiminished rhombicosidodecahedron is one of the Johnson solids (J80). It is also a canonical polyhedron.

Parabidiminished rhombicosidodecahedron
TypeJohnson
J79 - J80 - J81
Faces10 triangles
2×10 squares
10 pentagons
2 decagons
Edges90
Vertices50
Vertex configuration20(4.5.10)
10+20(3.4.5.4)
Symmetry groupD5d
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 opposing pentagonal cupolae removed. Related Johnson solids are the diminished rhombicosidodecahedron (J76) where one cupola is removed, the metabidiminished rhombicosidodecahedron (J81) where two non-opposing cupolae are removed and the tridiminished rhombicosidodecahedron (J83) where three cupolae are removed.

Example
Parabidiminished rhombicosidodecahedron
(Institute of Mathematics and Statistics, University of São Paulo)
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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.
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