Compound of four triangular prisms
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| Compound of four triangular prisms | |
|---|---|
| | |
| Type | Uniform compound |
| Index | UC 30 |
| 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 ( D 3 ) |
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.
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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
• citerefskilling1976Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society, 79 (3): 447–457, doi:10.1017/S0305004100052440, MR 0397554.