Gyrate rhombicosidodecahedron

In geometry, the gyrate rhombicosidodecahedron is one of the Johnson solids (J72). It is also a canonical polyhedron.

Gyrate rhombicosidodecahedron
TypeJohnson
J71 - J72 - J73
Faces4x5 triangles
4x5+10 squares
2+2x5 pentagons
Edges120
Vertices60
Vertex configuration10(3.42.5)
4x5+3x10(3.4.5.4)
Symmetry groupC5v
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 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.


Rhombicosidodecahedron
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.

gollark: But then everyone would steal the osmarkslisp™ one.
gollark: The first one was just "sort a list of integers".
gollark: Ah yes, fibonacci thing, very trivial.
gollark: I forgot what the last one was, but I can totally remember.
gollark: They all are that easy.
  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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