The Least-Perimeter Tile with n Faces
Seminar Room 1, Newton Institute
AbstractCo-authors: Paul Gallagher (University of Pennsylvania), Whan Ghang (MIT), David Hu (Georgetown University), Zane Martin (Williams College), Maggie Miller (University of Texas at Austin), Byron Perpetua (Williams College), Steven Waruhiu (University of Chicago)
The truncated octahedron is after Kelvin conjectured to be the least-surface-area unit-volume polyhedral tile of space. Work with undergraduates seeks the least-surface-area unit-volume n-hedral tile (with n faces). The solution is proved for only two values of n.
Related Links: http://arxiv.org/abs/1305.1590 - "Surface-area-minimizing n-hedral Tiles" preprint
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