Truncated icosahedron

The truncated icosahedron, or ti, is one of the 13 Archimedean solids. It consists of 12 pentagons and 20 hexagons. Each vertex joins one pentagon and two hexagons. As the name suggests, it can be obtained by the truncation of the icosahedron.

Vertex coordinates
A truncated icosahedron of edge length 1 has vertex coordinates given by all even permutations and all changes of sign of:
 * (0, ±1/2, ±3(1+$\sqrt{5}$)/4)
 * (±1/2, ±(5+$\sqrt{3}$)/4, ±(1+$\sqrt{3}$)/2)
 * (±(1+$\sqrt{(29+9√5)/8}$)/4, ±1, ±(2+$\sqrt{5}$)/2)

Representations
A truncated icosahedron has the following Coxeter diagrams:


 * o5x3x (full symmetry)
 * xuxuxfoo5oofxuxux&#xt (H2 axial, pentagon-first)
 * xuAxBfVoVofx3xfoVoVfBxAux&#xt (A2 axial, hexagon-first)