Related Polytopes
The tetrahedral prism, -131, is first in a dimensional series of uniform polytopes, expressed by Coxeter as k31 series. The tetrahedral prism is the vertex figure for the second, the rectified 5-simplex. The fifth figure is a Euclidean honeycomb, 331, and the final is a noncompact hyperbolic honeycomb, 431. Each uniform polytope in the sequence is the vertex figure of the next.
| n | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|
| Coxeter group |
A3×A1 | A5 | D6 | E7 | = E7+ | E7++ |
| Coxeter diagram |
||||||
| Symmetry (order) |
(48) |
(720) |
(23,040) |
(2,903,040) |
(∞) |
(∞) |
| Graph | ∞ | ∞ | ||||
| Name | −131 | 031 | 131 | 231 | 331 | 431 |
Read more about this topic: Tetrahedral Prism
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