Truncated tetrahedron

The truncated tetrahedron, or tut, is one of the 13 Archimedean solids. It consists of 4 triangles and 4 hexagons. 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 of
 * (±3$\sqrt{22}$/4, ±$\sqrt{2}$/4, ±$\sqrt{3}$/4).

Representations
A truncated tetrahedron has the following Coxeter diagrams:


 * x3x3o (full symmetry)
 * s4o3x (as triangle-alternated small rhombicuboctahedron)
 * xux3oox&#xt (A2 axial, triangle-first)
 * xuxo oxux&#xt (A1×A1 axial, edge-first)

Related polyhedra
It is possible to augment one of the hexagonal faces of the truncated tetrahedron with a triangular cupola to form the augmented truncated tetrahedron.

A number of uniform polyhedron compounds are composed of truncated tetrahedra:


 * Truncated stella octangula (2)
 * Truncated chiricosahedron (5)
 * Truncated icosicosahedron (10)