Surface-area-minimizing n-hedral Tiles
Paul Gallagher, Whan Ghang, David L. Hu, Zane Martin, Maggie Miller, Byron Perpetua, Steven Waruhiu · Rose-Hulman Scholar (Rose–Hulman Institute of Technology) · 2014
We provide a list of conjectured surface-area-minimizing n-hedral tiles of space for n from 4 to 14, previously known only for n equal to 5 and 6. We find the optimal "orientation-preserving" tetrahedral tile (n=4), and we give a nice new proof for the optimal 5-hedron (a triangular prism).