{"paper":{"title":"How many cages midscribe an egg?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.MG","authors_text":"Jinsong Liu, Ze Zhou","submitted_at":"2014-12-15T05:39:46Z","abstract_excerpt":"The Midscribability Theorem, which was first proved by O. Schramm, states that: given a strictly convex body $K\\subset\\mathbb{R}^{3}$ with smooth boundary and a convex polyhedron $P$, there exists a polyhedron $Q \\subset \\mathbb{RP}^3$ combinatorially equivalent to $P$ which midscribes $K$. Here the word \"midscribe\" means that all it's edges are tangent to the boundary surface of $K$.\n  By using of the intersection number technique, together with the Teichm\\\"{u}ller theory of packings, this paper provides an alternative approach to this theorem. Furthermore, combining Schramm's method with the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5430","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}