{"paper":{"title":"Spherical Foams in Flat Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.soft","authors_text":"Carl D. Modes, Randall D. Kamien","submitted_at":"2008-10-31T16:13:55Z","abstract_excerpt":"Regular tesselations of space are characterized through their Schlafli symbols {p,q,r}, where each cell has regular p-gonal sides, q meeting at each vertex, and r meeting on each edge. Regular tesselations with symbols {p,3,3} all satisfy Plateau's laws for equilibrium foams. For general p, however, these regular tesselations do not embed in Euclidean space, but require a uniform background curvature. We study a class of regular foams on S^3 which, through conformal, stereographic projection to R^3 define irregular cells consistent with Plateau's laws. We analytically characterize a broad clas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.5724","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"}