{"id":"openai-math/Finite-angular-cylinder-covers-below-the-half-area-bound","pdf":"https://github.com/openai/math/blob/main/preprints/Finite-angular-cylinder-covers-below-the-half-area-bound-September-27-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/Finite-angular-cylinder-covers-below-the-half-area-bound-September-27-2026","tags":["convex-geometry","cylinder-covering","tetrahedra"],"score":0,"title":"Finite angular cylinder covers below the half-area bound","domain":"Convex and metric geometry","family":"100","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MG","summary":"A regular tetrahedron admits a finite cylinder covering with compact triangular perpendicular bases whose total area is less than half its minimum orthogonal projection area. This disproves the half-area cylinder-covering conjecture. By affine invariance, the same construction gives a counterexample to the directionwise normalized half-bound for every nondegenerate tetrahedron.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-27","reactions":{},"formalized":false,"family_title":"Cylinder coverings below the half-area bound"}