Level: MSci
Title: Regular polyhedra and beyond
Supervisor:

Dr Matt Fayers
Research Area: Algebra
Description:

A polyhedron is a solid three-dimensional shape with flat faces, such as a cube. A polyhedron is regular if its faces are regular polygons and its vertices all look the same; the regular polyhedra were understood by the ancient Greeks. A polytope is like a polygon or polyhedron, but in any number of dimensions, and one can define a regular polytope in a suitable way via symmetries.

 

A student taking on this project would give an account of the classification of the regular polytopes, starting from Coxeter's classic (though rather old-fashioned) account. Then there is potential to explore some more of Coxeter's study of the geometry of these polytopes, or to look at some types of semi-regular polytopes, or perhaps (for the more combinatorially inclined) abstract regular polytopes.
Further Reading:
  • H. Coxeter, Regular polytopes. Dover, New York, 1973.
  • P. McMullen and E. Schulte, Regular abstract polytopes, Cambridge Univ. Press, 2002.
Key Modules:

MTH4103 Geometry I

MTH6104 Algebraic Structures II (essential)

MTH714U Group Theory (essential)
Other Information:
Current Availability: Yes