No torus with ten convex quadrilateral faces
No acoptic polyhedral torus in R3 has exactly 10 strictly convex quadrilateral faces. This is the F = 10 case of Grünbaum–Szilassi Conjecture 3.2; with Seamons's 11-face torus it settles which face counts occur. The proof reduces to the map {4,4}(3,1) and certifies, by an LRAT proof checked with the formally verified checker cake_lpr, that it has no planar strictly convex realisation, even allowing self-intersections. Code, certificates and a one-command checker: https://github.com/LeeMarshall1113/ai-math-results (results/torus-quad10).
Authors
- Lee Marshall
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-10-31
- DOI
- https://doi.org/10.5281/zenodo.23842783
- Primary Topic
- Advanced Combinatorial Mathematics
- Type
- preprint