Compound of ten truncated tetrahedraTypeUniform compoundIndexUC56Polyhedra10 truncated tetrahedraFaces40 triangles, 40 hexagonsEdges180Vertices120Symmetry groupicosahedral (Ih)Subgroup restricting to one constituentchiral tetrahedral (T) This uniform polyhedron compound is a composition of 10 truncated tetrahedra, formed by truncating each of the tetrahedra in the compound of 10 tetrahedra. It also results from composing the two enantiomers of the compound of 5 truncated tetrahedra. It could also be called a truncated icosicosahedron.
Cartesian coordinates Cartesian coordinates for the vertices of this compound are all the even permutations of
(±1, ±1, ±3) (±τ−1, ±(−τ−2), ±2τ) (±τ, ±(−2τ−1), ±τ2) (±τ2, ±(−τ−2), ±2) (±(2τ−1), ±1, ±(2τ − 1))
where τ = (1+)/2 is the golden ratio (sometimes written φ).
References .