Uniform 10-polytope - Uniform 10-polytopes By Fundamental Coxeter Groups

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:

  1. Simplex family: A10 -
    • 527 uniform 10-polytopes as permutations of rings in the group diagram, including one regular:
      1. {39} - 10-simplex -
  2. Hypercube/orthoplex family: B10 -
    • 1023 uniform 10-polytopes as permutations of rings in the group diagram, including two regular ones:
      1. {4,38} - 10-cube or dekeract -
      2. {38,4} - 10-orthoplex or decacross -
      3. h{4,38} - 10-demicube .
  3. Demihypercube D10 family: -
    • 767 uniform 10-polytopes as permutations of rings in the group diagram, including:
      1. 17,1 - 10-demicube or demidekeract -
      2. 71,1 - 10-orthoplex -

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