Compound of four triangular prisms
{{Short description|Polyhedral compound}}
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!bgcolor=#e7dcc3 colspan=2|Compound of four triangular prisms | |
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| bgcolor=#e7dcc3|Type | Uniform compound |
| bgcolor=#e7dcc3|Index | UC30 |
| bgcolor=#e7dcc3|Polyhedra | 4 triangular prisms |
| bgcolor=#e7dcc3|Faces | 8 triangles, 12 squares |
| bgcolor=#e7dcc3|Edges | 36 |
| bgcolor=#e7dcc3|Vertices | 24 |
| bgcolor=#e7dcc3|Symmetry group | chiral octahedral (O) |
| bgcolor=#e7dcc3|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+{{radic|2}}), ±(1−{{radic|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
- {{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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