Compound of five truncated tetrahedraTypeUniform compoundIndexUC55Polyhedra5 truncated tetrahedraFaces20 triangles, 20 hexagonsEdges90Vertices60DualCompound of five triakis tetrahedraSymmetry groupchiral icosahedral (I)Subgroup restricting to one constituentchiral tetrahedral (T)
The compound of five truncated tetrahedra is a uniform polyhedron compound. It's composed of 5 truncated tetrahedra rotated around a common axis. It may be formed by truncating each of the tetrahedra in the compound of five tetrahedra. A far-enough truncation creates the compound of five octahedra. Its convex hull is a nonuniform snub dodecahedron. It could also be called a truncated chiricosahedron.
Cartesian coordinates Cartesian coordinates for the vertices of this compound are all the cyclic permutations of
(±1, ±1, ±3) (±τ−1, ±(−τ−2), ±2τ) (±τ, ±(−2τ−1), ±τ2) (±τ2, ±(−τ−2), ±2) (±(2τ−1), ±1, ±(2τ − 1))
with an even number of minuses in the choices for '±', where τ = (1+)/2 is the golden ratio (sometimes written φ).
References .