Parabigyrate rhombicosidodecahedron

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.

Parabigyrate rhombicosidodecahedron
Parabigyrate rhombicosidodecahedron.png
TypeJohnson
J72 - J73 - J74
Faces2x10 triangles
3x10 squares
2+10 pentagons
Edges120
Vertices60
Vertex configuration20(3.42.5)
2x10+20(3.4.5.4)
Symmetry groupD5d
Dual polyhedron-
Propertiesconvex
Net
Johnson solid 73 net.png

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: the gyrate rhombicosidodecahedron (J72) where only one cupola is rotated, the metabigyrate rhombicosidodecahedron (J74) where two non-opposing cupolae are rotated and the trigyrate rhombicosidodecahedron (J75) where three cupolae are rotated.

External linksEdit

  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.