Compound of five truncated tetrahedra

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Compound of five truncated tetrahedra
UC55-5 truncated tetrahedra.png
Type Uniform compound
Index UC55
Polyhedra 5 truncated tetrahedra
Faces 20 triangles, 20 hexagons
Edges 90
Vertices 60
Dual Compound of five triakis tetrahedra
Symmetry group chiral icosahedral (I)
Subgroup restricting to one constituent chiral tetrahedral (T)

This uniform polyhedron compound is a composition of 5 truncated tetrahedra, formed by truncating each of the tetrahedra in the compound of 5 tetrahedra. A far-enough truncation creates the Compound of five octahedra. Its convex hull is a nonuniform Snub dodecahedron.

Cartesian coordinates[edit]

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+√5)/2 is the golden ratio (sometimes written φ).


  • Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society, 79: 447–457, doi:10.1017/S0305004100052440, MR 0397554 .