# Van Oss polygon

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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.