Great rhombicuboctahedron

This page is about the convex polyhedron also known as the truncated cuboctahedron. For the non-convex conjugate of the small rhombicuboctahedron, see quasirhombicuboctahedron.

}} The great rhombicuboctahedron, also commonly known as the truncated cuboctahedron, or girco is one of the 13 Archimedean solids. It consists of 6 octagons, 8 hexagons, and 12 square, with one of each type of face meeting per vertex. It can be obtained by cantitruncation of the cube or octahedron, or equivalently by truncating the vertices of a cuboctahedron and then adjusting the edge lengths to be all equal.
 * angle = 6-4: acos(–$\sqrt{13+6√2}$/3) ≈ 144.73561º 8-4: 135º 8-6: acos(–$\sqrt{2}$/3) ≈ 125.26439º
 * dual = Disdyakis dodecahedron
 * conjugate = Quasitruncated cuboctahedron

Vertex coordinates
A great rhombicuboctahedron of edge length 1 has vertex coordinates given by all permutations and sign changes of
 * (±(1+2$\sqrt{2}$)/2, ±(1+$\sqrt{3}$)/2, ±1/2).