Parabigyrate rhombicosidodecahedron

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Parabigyrate rhombicosidodecahedron
Parabigyrate rhombicosidodecahedron.png
Type Johnson
J72J73J74
Faces 2x10 triangles
3x10 squares
2+10 pentagons
Edges 120
Vertices 60
Vertex configuration 20(3.42.5)
2x10+20(3.4.5.4)
Symmetry group D5d
Dual polyhedron -
Properties convex, canonical
Net
Johnson solid 73 net.png

In geometry, the parabigyrate rhombicosidodecahedron is one of the Johnson solids (J73). It can be constructed as a rhombicosidodecahedron with two opposing pentagonal cupolae rotated through 36 degrees. It is also a canonical polyhedron.

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]

Alternative Johnson solids, constructed by rotating different cupolae of a rhombicosidodecahedron, 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 .

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Trigyrate rhombicosidodecahedron 75th Johnson solid

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Metagyrate diminished rhombicosidodecahedron 78th Johnson solid

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