Trigyrate rhombicosidodecahedron

Trigyrate rhombicosidodecahedron
Type	Johnson J74 - J75 - J76
Faces	2+2x3+2x6 triangles 4x3+3.6 squares 4x3 pentagons
Edges	120
Vertices	60
Vertex configuration	5x6(3.42.5) 4x3+3x6(3.4.5.4)
Symmetry group	C3v
Dual polyhedron	-
Properties	convex
Net

In geometry, the trigyrate rhombicosidodecahedron is one of the Johnson solids (J₇₅). It can be constructed as a rhombicosidodecahedron with three pentagonal cupolae rotated through 36 degrees. Related Johnson solids are the gyrate rhombicosidodecahedron (J₇₂) where one cupola is rotated, the parabigyrate rhombicosidodecahedron (J₇₃) where two opposing cupolae are rotated and the metabigyrate rhombicosidodecahedron (J₇₄) where two non-opposing cupolae are rotated.

The 92 Johnson solids were named and described by Norman Johnson in 1966.

References

• Norman W. Johnson, "Convex Solids with Regular Faces", Canadian Journal of Mathematics, 18, 1966, pages 169–200. Contains the original enumeration of the 92 solids and the conjecture that there are no others.
• Victor A. Zalgaller (1969). Convex Polyhedra with Regular Faces. Consultants Bureau. No ISBN.  The first proof that there are only 92 Johnson solids.

External links

• Weisstein, Eric W., "Johnson Solid", MathWorld.
  • Weisstein, Eric W., "Trigyrate rhombicosidodecahedron", MathWorld.