Uniform 10-polytopes By Fundamental Coxeter Groups
Uniform 10-polytopes with reflective symmetry can be generated by these three Coxeter groups, represented by permutations of rings of the Coxeter-Dynkin diagrams:
| # | Coxeter group | Coxeter-Dynkin diagram | |
|---|---|---|---|
| 1 | A10 | ||
| 2 | B10 | ||
| 3 | D10 | ||
Selected regular and uniform 10-polytopes from each family include:
- Simplex family: A10 -
- 527 uniform 10-polytopes as permutations of rings in the group diagram, including one regular:
- {39} - 10-simplex -
- 527 uniform 10-polytopes as permutations of rings in the group diagram, including one regular:
- Hypercube/orthoplex family: B10 -
- 1023 uniform 10-polytopes as permutations of rings in the group diagram, including two regular ones:
- {4,38} - 10-cube or dekeract -
- {38,4} - 10-orthoplex or decacross -
- h{4,38} - 10-demicube .
- 1023 uniform 10-polytopes as permutations of rings in the group diagram, including two regular ones:
- Demihypercube D10 family: -
- 767 uniform 10-polytopes as permutations of rings in the group diagram, including:
- 17,1 - 10-demicube or demidekeract -
- 71,1 - 10-orthoplex -
- 767 uniform 10-polytopes as permutations of rings in the group diagram, including:
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