Details

"Tilings on Polyhedra and Polyhedra on Tilings"

A talk in two acts. In the first act, "Tilings on Polyhedra," we count a family of tilings first enumerated by the artist M. C. Escher, and then lift these questions into three dimensions. This allows us to answer questions such as: How many ways can we arrange panels on a soccer ball?
The second act, "Polyhedra on Tilings," focuses on joint work with Prof. Andrés, describing an algorithm to count “generalized polyforms.” This algorithm counts objects such as the number of pieces in the (166 + 4)-piece 3D puzzle Hexacube, donated to the HMC Math Department by HMC alum Andy Niedermaier ’04, or the number of ways to arrange the building blocks of TOWARD, a temporary sculpture built in 2024 outside of Jacobs.