An explicit finite cylinder cover of the regular tetrahedron saving 3.86×10⁻⁴ below the half-area bound
Year: 2026
Type: preprint
Abstract: We give an explicit cover of a regular tetrahedron by 4096 cylinders with compact triangular perpendicular bases. The sum of their base areas, divided by the tetrahedron's minimum orthogonal projection area, lies in [0.499613830783714148, 0.499613830783714149). Thus the saving below 1/2 exceeds 0.000386169216285851. The construction uses a finite tilt in the angular-sector framework of OpenAI's September 2026 preprint and rationally specified radial cutoffs. Coverage is certified by exact linear-programming dual witnesses, and independently verified by exhaustive rational polyhedron clipping. We describe the geometric reduction, the certificate obligations, and reproducible verification of the full closed tetrahedron and the perpendicular base areas. No optimality is asserted.
Author: Pinho, Ricardo
Language: English
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222966552
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