Title

Classifying Regular Polytopes in Dimension 4 and Beyond

Date

5-31-2018 1:40 PM

End Time

31-5-2018 2:00 PM

Location

HWC 204

Session Chair

Cheryl Beaver

Session Chair

Leanne Merrill

Session Title

Mathematics Capstone Project Presentations

Presentation Type

Presentation

Faculty Sponsor(s)

Leanne Merrill

Abstract

It is well-known that there exists infinitely many regular convex polygons, and that there exists exactly five regular convex polyhedra, more commonly known as the Platonic solids. We seek to prove these facts and to extend our findings to higher dimension polytopes such that for any dimension n, we can state and prove how many regular convex n-polytopes there are. We will also explore the classification of nonconvex polytopes, commonly known as star polytopes.

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May 31st, 1:40 PM May 31st, 2:00 PM

Classifying Regular Polytopes in Dimension 4 and Beyond

HWC 204

It is well-known that there exists infinitely many regular convex polygons, and that there exists exactly five regular convex polyhedra, more commonly known as the Platonic solids. We seek to prove these facts and to extend our findings to higher dimension polytopes such that for any dimension n, we can state and prove how many regular convex n-polytopes there are. We will also explore the classification of nonconvex polytopes, commonly known as star polytopes.