Compound of four triangular prisms
Polyhedral compound
Compound of four triangular prisms | |
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Type | Uniform compound |
Index | UC30 |
Polyhedra | 4 triangular prisms |
Faces | 8 triangles, 12 squares |
Edges | 36 |
Vertices | 24 |
Symmetry group | chiral octahedral (O) |
Subgroup restricting to one constituent | 3-fold dihedral (D3) |
This uniform polyhedron compound is a chiral symmetric arrangement of 4 triangular prisms, aligned with the axes of three-fold rotational symmetry of an octahedron.
Cartesian coordinates
Cartesian coordinates for the vertices of this compound are all the even permutations of
- (±1, ±(1+√2), ±(1−√2))
with an even number of minuses in the '±' choices, together with all the odd permutations with an odd number of minuses in the '±' choices.
References
- Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society, 79: 447–457, doi:10.1017/S0305004100052440, MR 0397554.
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