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).
Prof. Frank Morgan, Department of Mathematics, Williams College
Gallagher, Paul; Ghang, Whan; Hu, David; Martin, Zane; Miller, Maggie; Perpetua, Byron; and Waruhiu, Steven
"Surface-area-minimizing n-hedral Tiles,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 15
, Article 13.
Available at: http://scholar.rose-hulman.edu/rhumj/vol15/iss1/13