{"id":"hexagon/2610.00210","pdf":"https://hexagonmath.org/pdf/2610.00210v1","url":"https://hexagonmath.org/abs/2610.00210v1","tags":["msc:52B60","computer-assisted proof","isoperimetric inequality","translational tiling"],"score":0,"title":"The truncated octahedral conjecture","domain":"math.MG","origin":"ai-generated","source":"hexagon","authors":["Thomas Hales","Lark Song"],"reviews":0,"subject":"math.MG","summary":"Among three-dimensional parallelohedra of fixed volume, the Archimedean truncated octahedron uniquely minimizes surface area, affirming a conjecture of K. Bezdek from 2006. One inequality in the proof is verified by an exact computer-assisted certificate. The simplex, frame, and graphical-zonotope inequalities used in the proof hold in arbitrary dimension.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT"],"discussed":0,"published":"2026-10-12","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"all"}