Truncated tetrahedron

The truncated tetrahedron is one of the 13 Archimedean solids. It consists of 4 hexagons and 4 triangles. Each vertex joins one triangle and two hexagons. As the name suggests, it can be obtained by truncation of the tetrahedron.

Vertex coordinates
A truncated tetrahedron of edge length 1 has vertex coordinates given by all even permutations and sign changes of
 * (±3$\sqrt{22}$/4, ±$\sqrt{2}$/4, ±$\sqrt{3}$/4).