# COLLOQUIUM

## Classification of Convex N-Dimensional Regular Polytopes, Euclidean Honeycombs, and Hyperbolic Honeycombs

### Annie Oppman

M.S. Defense, advised by Fredric Ancel

**Friday, June 18, 2010, 12:00 pm, EMS E423**

A polytope is a geometric figure bounded by portions of lines, planes, or hyperplanes. Polytopes exist in every dimension. H.S.M Coxeter has written many books and papers focusing on the geometric properties of polytopes. In this paper we will use definitions and methods presented in Coxeter's book /Regular Polytopes/ and his paper "Regular Honeycombs in Hyperbolic Space", to classify the convex regular polytopes, Euclidean honeycombs, and hyperbolic honeycombs. We will also fill in many of the details of finding these classifications that were left to the reader in both the book and the paper.

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