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Face Numbers and Angles of Polytopes

Josh Hinman, University of Washington
Wednesday, October 4, 2023 - 3:30pm to 5:00pm
PDL C-401 and via Zoom Link:


Picture your favorite \$d\$-dimensional polytope. It has faces of every dimension below \$d\$: zero-dimensional vertices, one-dimensional edges, two-dimensional polygons, and so on. Counting the faces of each dimension yields a list of face numbers. For example, a \$3\$-cube has face numbers \$(8, 12, 6)\$: eight vertices, twelve edges, and six facets.

What integer tuples can arise as the face numbers of a polytope? Geometric methods may help us answer this question. In my talk, I'll discuss what we can learn about the face numbers of polytopes from their geometric properties--specifically, their angles. I'll present a set of tight linear inequalities on face numbers, answering a 1997 question of Bárány.

Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.

Join Zoom Meeting:
Meeting ID: 915 4733 5974