compound of five truncated tetrahedra
{{Short description|Polyhedral compound}}
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!bgcolor=#e7dcc3 colspan=2|Compound of five truncated tetrahedra | |
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| bgcolor=#e7dcc3|Type | Uniform compound |
| bgcolor=#e7dcc3|Index | UC55 |
| bgcolor=#e7dcc3|Polyhedra | 5 truncated tetrahedra |
| bgcolor=#e7dcc3|Faces | 20 triangles, 20 hexagons |
| bgcolor=#e7dcc3|Edges | 90 |
| bgcolor=#e7dcc3|Vertices | 60 |
| bgcolor=#e7dcc3|Dual | Compound of five triakis tetrahedra |
| bgcolor=#e7dcc3|Symmetry group | chiral icosahedral (I) |
| bgcolor=#e7dcc3|Subgroup restricting to one constituent | chiral tetrahedral (T) |
File:Compound of five truncated tetrahedra.stl
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), ±τ2)
: (±τ2, ±(−τ−2), ±2)
: (±(2τ−1), ±1, ±(2τ − 1))
with an even number of minuses in the choices for '±', where τ = (1+{{radic|5}})/2 is the golden ratio (sometimes written φ).
References
- {{citation|first=John|last=Skilling|title=Uniform Compounds of Uniform Polyhedra|journal=Mathematical Proceedings of the Cambridge Philosophical Society|volume=79|issue=3|pages=447–457|year=1976|doi=10.1017/S0305004100052440|mr=0397554}}.
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