# Degenerate polytope

A polytope is informally dubbed **degenerate** when it satisfies certain undesirable properties. These might possibly include coplanar, or coincident elements, skew elements, non-dyadicity, or being fissary.

## Definitions[edit | edit source]

There is currently no single definition for what it means for a shape to be degenerate. As such, this term is ambiguous in formal discussion, unless the specific cases for which the term will be used are agreed upon beforehand.

### McMullen and Schulte[edit | edit source]

In their study of abstract polytopes McMullen and Schulte define a polytope 𝓟 to be **degenerate** if an adjacent pair of its distinguished generators commute.^{[1]} That is if there is a pair of generators and such that .

For regular polytopes this is exactly those polytopes that have a 2 in their Schläfli type.

The *Atlas of Small Regular Polytopes* also uses this definition.

## References[edit | edit source]

- ↑ McMullen (2007:357)

## Bibliography[edit | edit source]

- McMullen, Peter (2007). "Four-Dimensional Regular Polyhedra" (PDF).
*Discrete & Computational Geometry*.

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