{"paper":{"title":"Integral regular truncated pyramids with rectangular bases and the diophantine equation x^2+y^2+z^2= t^2","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Konstantine Zelator","submitted_at":"2012-10-23T19:39:38Z","abstract_excerpt":"A regular truncated pyramid with rectangular bases;consists of two rectangular bases whose centers are orthogonally aligned with respect to the parallel planes containing their bases; and two pairs of congruent isosceles trapezoids(the four lateral faces). Thrre are six lengths involved:the larger base dimensions a and b; a>(or=)b. The smaller base dimensions c and d; c>(or=d). The height H, and the common length t of the four lateral faces. When a,b,c,d,H,t, and the volume V are all positive integers; we have an integral regular truncated pyramid with rectangular bases(see Definition 1 in the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6836","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"}