Compound of five stellated truncated cubes
From Wikipedia, the free encyclopedia
Compound of five stellated truncated cubes | |
---|---|
Type | Uniform compound |
Index | UC58 |
Polyhedra | 5 stellated truncated cubes |
Faces | 40 triangles, 30 octagrams |
Edges | 180 |
Vertices | 120 |
Symmetry group | icosahedral (Ih) |
Subgroup restricting to one constituent | pyritohedral (Th) |
This uniform polyhedron compound is a composition of 5 stellated truncated cubes, formed by star-truncating each of the cubes in the compound of 5 cubes.
[edit] Cartesian coordinates
Cartesian coordinates for the vertices of this compound are all the cyclic permutations of
- (±(2−√2), ±√2, ±(2−√2))
- (±τ, ±(τ−1−τ−1√2), ±(2τ−1−τ√2))
- (±1, ±(τ−2+τ−1√2), ±(τ2−τ√2))
- (±(1−√2), ±(−τ−2+√2), ±(τ2−√2))
- (±(τ−τ√2), ±(−τ−1), ±(2τ−1−τ−1√2))
where τ = (1+√5)/2 is the golden ratio (sometimes written φ).
[edit] References
- John Skilling, Uniform Compounds of Uniform Polyhedra, Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 79, pp. 447-457, 1976.