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
Famous quotes containing the word related:
“There is nothing but is related to us, nothing that does not interest us,—kingdom, college, tree, horse, or iron show,—the roots of all things are in man.”
—Ralph Waldo Emerson (1803–1882)
Related Phrases
Related Words