Normality of smooth lattice three-polytopes
Mateusz Michalek·Chat GPT Sol·Claude Fable and Opus
Abstract
We prove that every smooth lattice three-polytope is normal, settling Oda’s normality question in dimension three. By Ogata–Nakagawa stabilization it suffices to prove 2-normality. A hypothetical hole produces a minimal centrally symmetric strip body disjoint from the lattice, with three or four strip pairs and all nonzero lattice widths at least three. The four-strip case is excluded by Howe’s theorem, Pick’s formula and Ball’s plank theorem; the three-strip case reduces to a sharp 3 × 3 matrix inequality proved by exact case analysis in the appendix.Discussion
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