Paragyrate diminished rhombicosidodecahedron

Paragyrate diminished rhombicosidodecahedron
TypeJohnson
J76 – J77 – J78
Faces3x5 triangles
3x5+10 squares
1+2x5 pentagons
1 decagon
Edges105
Vertices55
Vertex configuration10(4.5.10)
10(3.42.5)
3x5+2.10(3.4.5.4)
Symmetry groupC5v
Dual polyhedron-
Propertiesconvex
Net

In geometry, the paragyrate diminished rhombicosidodecahedron is one of the Johnson solids (J77). It can be constructed as a rhombicosidodecahedron with one pentagonal cupola rotated through 36 degrees, and the opposing pentagonal cupola removed.

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]

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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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