Gyrate rhombicosidodecahedron
Type	Johnson J71 – J72 – J73
Faces	20 triangles 30 squares 12 pentagons
Edges	120
Vertices	60
Vertex configuration	10(3.42.5) 4x5+3x10(3.4.5.4)
Symmetry group	C5v
Dual polyhedron	-
Properties	convex, canonical
Net

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

Related polyhedron

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.