Gordon Williams
Topic Areas:
Geometry, polyhedra, convex or abstract polytopes, convexity, Euler's Theorem, recreational mathematics.
Prepared Talks:
- Generalizing Polyhedra: Beyond Convexity
- We will explore some of the exciting recent history of the study of polyhedra and polytopes, in particular efforts to generalize the theory to the study of non-convex bodies including topics such as the recently solved Bellows Conjecture.
- How to deflate a chicken and fill space
- We will explore some of the surprising connections between Penrose tiles, fractal geometry, the Fibonacci sequence and space filling curves.
- Petrie Polygons and Petrie Schemes
- For polyhedra, a Petrie polygon is a path along the edges such that each pair of consecutive edges share an edge, but not three. On the Platonic solids these paths look like equators. Petrie polygons have been useful in the study of regular polytopes and of Coxeter groups. This talk explores the speaker's work on extending the notion of a Petrie polygon to higher dimensions and more general structures such as abstract poltyopes and simplicial spheres.
- Abstract Archimedean Polyhedra
- This talk explores joint work with M. Hartley on the representation of the familiar Archimedean polyhedra as quotients of regular abstract polytopes.
Contact Information:
- Institution: Ursinus College
- Phone Number: 610-409-3000 x2997
- e-Mail Address: gwilliams@ursinus.edu
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