Metabigyrate rhombicosidodecahedron

In geometry, the metabigyrate rhombicosidodecahedron is one of the Johnson solids (J₇₄). It can be constructed as a rhombicosidodecahedron with two non-opposing pentagonal cupolae rotated through 36 degrees. It is also a canonical polyhedron.

Metabigyrate rhombicosidodecahedron
Type	Johnson J73 – J74 – J75
Faces	4x2+3x4 triangles 2+2x2+6x4 squares 4x2+4 pentagons
Edges	120
Vertices	60
Vertex configuration	5.4(3.42.5) 4x2+8x4(3.4.5.4)
Symmetry group	C2v
Dual polyhedron	-
Properties	convex, canonical
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]

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

• The gyrate rhombicosidodecahedron (J₇₂) where only one cupola is rotated;
• The parabigyrate rhombicosidodecahedron (J₇₃) where two opposing cupolae are rotated;
• And the trigyrate rhombicosidodecahedron (J₇₅) where three cupolae are rotated.

External links

• Weisstein, Eric W., "Metabigyrate rhombicosidodecahedron" ("Johnson solid") at MathWorld.
• World of Polyhedra - metabigyrate rhombicosidodecahedron (interactive rotatable wireframe applet)

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.