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 -

Read more about this topic:  Uniform 10-polytope

Famous quotes containing the words uniform, fundamental and/or groups:

    “Truly man is a marvelously vain, diverse, and undulating object. It is hard to found any constant and uniform judgment on him.”
    —Michel de Montaigne (1533–1592)

    “Two fundamental literary qualities: supernaturalism and irony.”
    —Charles Baudelaire (1821–1867)

    “Belonging to a group can provide the child with a variety of resources that an individual friendship often cannot—a sense of collective participation, experience with organizational roles, and group support in the enterprise of growing up. Groups also pose for the child some of the most acute problems of social life—of inclusion and exclusion, conformity and independence.”
    —Zick Rubin (20th century)