Department of Mathematics

Combinatorics and Graph Theory

  •  Proving the Least-Area Tetrahedral Tile of Space
  •  11/14/2017
  •  4:10 PM - 5:00 PM
  •  C304 Wells Hall
  •  Eliot Bongiovanni, Michigan State Universtiy

We prove the least-area, unit-volume, tetrahedral tile of Euclidean space, without the assumption that the tiling uses only orientation-preserving images of the tile. Using a graph-theoretical approach, we define a class of tetrahedra that potentially tile with less surface area than the orientation-preserving minimizer, the Sommerville No. 1. We find that without the assumption of orientation preservation, the winner remains the Sommerville No. 1. The talk summarizes "The Least-Area Tetrahedral Tile of Space" by Eliot Bongiovanni, Alejandro Diaz, Arjun Kakkar, and Nat Sothanaphan, a product of the 2017 NSF Williams College SMALL REU. Preprint: https://arxiv.org/abs/1709.04139

 

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Department of Mathematics
Michigan State University
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