Gyrate rhombicosidodecahedron

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Gyrate rhombicosidodecahedron
Gyrate rhombicosidodecahedron.png
Type Johnson
J71 - J72 - J73
Faces 4x5 triangles
4x5+10 squares
2+2x5 pentagons
Edges 120
Vertices 60
Vertex configuration 10(3.42.5)
4x5+3x10(3.4.5.4)
Symmetry group C5v
Dual polyhedron -
Properties convex
Net
Johnson solid 72 net.png

In geometry, the gyrate rhombicosidodecahedron is one of the Johnson solids (J72).

A Johnson solid is one of 92 strictly convex polyhedra that have regular faces but are not uniform (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]

Related polyhedron[edit]

It can be constructed as a rhombicosidodecahedron with one pentagonal cupola rotated through 36 degrees. They have the same faces around each vertex, but vertex configurations along the rotation become a different order, 3.4.4.5.

Small rhombicosidodecahedron.png
Rhombicosidodecahedron
Gyrate rhombicosidodecahedron color.png
Gyrate rhombicosidodecahedron

Alternative Johnson solids, constructed by rotating different cupolae of a rhombicosidodecahedron, are: the parabigyrate rhombicosidodecahedron (J73) where two opposing cupolae are rotated, the metabigyrate rhombicosidodecahedron (J74) where two non-opposing cupolae are rotated and the trigyrate rhombicosidodecahedron (J75) where three cupolae are rotated.

External links[edit]

  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 .