{"paper":{"title":"On bodies with directly congruent projections and sections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.MG","authors_text":"Dmitry Ryabogin, M. Angeles Alfonseca, Michelle Cordier","submitted_at":"2014-12-08T20:33:21Z","abstract_excerpt":"Let $K$ and $L$ be two convex bodies in ${\\mathbb R^4}$, such that their projections onto all $3$-dimensional subspaces are directly congruent. We prove that if the set of diameters of the bodies satisfy an additional condition and some projections do not have certain symmetries, then $K$ and $L$ coincide up to translation and an orthogonal transformation. We also show that an analogous statement holds for sections of star bodies, and prove the $n$-dimensional versions of these results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2727","kind":"arxiv","version":2},"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"}