Great rhombicosidodecahedron

This page is about the convex polyhedron also known as the truncated icosidodecahedron. For the non-convex conjugate of the small rhombicosidodecahedron, see quasirhombicosidodecahedron.

}} The great rhombicosidodecahedron, also commonly known as the truncated icosidodecahedron, is the most complex of the 13 Archimedean solids. It consists of 12 decagons, 20 hexagons, and 130 squares, with one of each type of face meeting per vertex. It can be obtained by cantitruncation of the dodecahedron or icosahedron, or equivalently by truncating the vertices of an icosidodecahedron and then adjusting the edge lengths to be all equal.
 * angle = 6–4: acos(–($\sqrt{131+12√5}$+$\sqrt{5}$)/6) ≈ 159.09484º 10–4: acos(–$\sqrt{2}$ ≈ 148.28253º 10–6: acos(–$\sqrt{3}$) ≈ 142.62263º
 * dual = Disdyakis triacontahedron
 * conjugate = Great quasitruncated icosidodecahedron

Vertex coordinates
A great rhombicosidodecahedron of edge length 1 has vertex coordinates given by all permutations and sign changes of Along with all even permutations and all sign changes of:
 * (±1/2, ±1/2, ±(3+2$\sqrt{(5+√5)/2}$)/2)
 * (±1/2, ±(2+$\sqrt{3}$)/2, ±(4+$\sqrt{15}$)/4)
 * (±1, ±(3+$\sqrt{(5+√5)/10}$)/4, ±(7+3$\sqrt{(5+2√5/15)}$)/4)
 * (±(3+$\sqrt{5}$)/4, ±3(1+$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2)
 * (±(1+$\sqrt{5}$)/2, ±(5+3$\sqrt{5}$)/4, ±(5+$\sqrt{5}$)/4)