Van Oss polygon

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The Van Oss polygon of an octahedron is a square.

The Van Oss polygon of a polytope is a particular kind of pseudo-face.

Van Oss polygons have an important role in the enumeration of the regular complex polytopes and the regular star polytopes.

Definition[edit | edit source]

The Van Oss polygon is defined for regular polytopes with an r -symmetric vertex figure. Given 𝓟, satisfying this requirement, its Van Oss polygon is the cross-section of 𝓟 with the plane O 0 O n O 1 , where:

  • O 0  is an arbitrary vertex of the polytope
  • O 1  is the midpoint of an edge adjacent to O 0 
  • O n  is the center of the polytope

See also[edit | edit source]

Bibliography[edit | edit source]

  • Coxeter, Donald (1974). Regular complex polytopes. Cambridge University Press. ISBN 0-521-39490-2.