Compound of five truncated tetrahedra
# Compound of five truncated tetrahedra

Compound of five truncated tetrahedra :

| Type | Uniform compound |
| - | - |
| Index | $UC_{55}$ |
| 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) |

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.

## 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, $±(−2τ^{−1}),$ $±τ^2)$
    $(±τ^2,$ $±(−τ^{−2}),$ ±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).

