truncated icosidodecahedron

From truncated + icosidodecahedron, referring to a partial construction method for the figure. (The resultant figure requires further distortion to make the faces regular.)

truncated icosidodecahedron (plural truncated icosidodecahedra or truncated icosidodecahedrons)

1. An Archimedean solid with 62 regular faces (12 decagons, 20 hexagons and 30 squares) and 180 edges.
   • 1961, The New Yorker, Volume 37, Part 4, page 172:

     The Solid Shapes Lab, another Science Materials Center contribution to future mathematicians, together to form not only regular polyhedrons but rhombicosidodecahedrons, truncated icosidodecahedrons, and such.

   • 1962, The Mineralogical Magazine and Journal of the Mineralogical Society, volume 33, page 1008:

     The truncated icosahedron and truncated icosidodecahedron have fivefold symmetry and cannot four four-connected frameworks with lattice symmetry.

   • 2007, Numerical Analysis and Applied Mathematics: International Conference of Numerical Analysis and Applied Mathematics, page 95:

     It is also a Catalan solid, the disdyakis triacontahedron, dual of the truncated icosidodecahedron.

The term truncated icosidodecahedron is considered improper by some authors because the implied construction results in a figure whose faces are not regular, and further distortion is required to make them so. The synonym great rhombicosidodecahedron is thus often preferred, even though confusion may arise with the (small) rhombicosidodecahedron and the nonconvex great rhombicosidodecahedron.

• (polyhedron with 12 decagonal, 30 hexagonal and 30 square faces): great rhombicosidodecahedron, rhombitruncated icosidodecahedron

• great truncated icosidodecahedron

• Great Rhombicosidodecahedron on Wolfram MathWorld