2 papers
math.MG2026
Local quadratic isoperimetric stability of the truncated octahedron among parallelohedra
Lark Song
We prove that the Archimedean truncated octahedron is a strict local minimizer of the isoperimetric quotient among all parallelohedra in . After volume normalization…
math.MG2026
The Truncated Octahedral Conjecture
Thomas Hales, Lark Song
Among three-dimensional parallelohedra of fixed volume, the Archimedean truncated octahedron uniquely minimizes surface area, affirming a conjecture of K. Bezdek from 2006. The fin…