Sam Hsiao - Bard College
Combinatorics and Applications of Polytopes
A polytope is a higher dimensional generalization of a polygon. Examples of 3-dimensional polytopes include cubes, pyramids, and prisms. The study of polytopes dates back to ancient Greek geometry. In more recent years polytopes have been intensively studied from the viewpoint of industrial applications. This has invigorated basic research on the combinatorial properties of polytopes. For example, questions about "face numbers" are an active topic of research in combinatorics (the face numbers of a cube are [8, 12, 6] because a cube has 8 vertices, 12 edges, and 6 facets). This talk will introduce students to the combinatorics and applications of polytopes. There will be mention of some open questions about face numbers.
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