{"product_id":"9783031475108","title":"Reshaping Convex Polyhedra","description":"\u003cp\u003e^ the=\"\" study=\"\" of=\"\" convex=\"\" polyhedra=\"\" in=\"\" ordinary=\"\" space=\"\" is=\"\" a=\"\" central=\"\" piece=\"\" classical=\"\" and=\"\" modern=\"\" geometry=\"\" that=\"\" has=\"\" had=\"\" significant=\"\" impact=\"\" on=\"\" many=\"\" areas=\"\" mathematics=\"\" also=\"\" computer=\"\" science.=\"\" present=\"\" book=\"\" project=\"\" by=\"\" joseph=\"\" o’rourke=\"\" costin=\"\" vîlcu=\"\" brings=\"\" together=\"\" two=\"\" important=\"\" strands=\"\" subject=\"\" —=\"\" combinatorics=\"\" polyhedra,=\"\" intrinsic=\"\" underlying=\"\" surface.=\"\" this=\"\" leads=\"\" to=\"\" remarkable=\"\" interplay=\"\" concepts=\"\" come=\"\" life=\"\" wide=\"\" range=\"\" very=\"\" attractive=\"\" topics=\"\" concerning=\"\" polyhedra.=\"\" gets=\"\" message=\"\" across=\"\" thetheory=\"\" although=\"\" with=\"\" roots,=\"\" still=\"\" much=\"\" alive=\"\" today=\"\" continues=\"\" be=\"\" inspiration=\"\" basis=\"\" lot=\"\" current=\"\" research=\"\" activity.=\"\" work=\"\" presented=\"\" manuscript=\"\" interesting=\"\" applications=\"\" discrete=\"\" computational=\"\" geometry,=\"\" as=\"\" well=\"\" other=\"\" mathematics.=\"\" treated=\"\" detail=\"\" include=\"\" unfolding=\"\" onto=\"\" surfaces,=\"\" continuous=\"\" flattening=\"\" convexity=\"\" theory=\"\" minimal=\"\" length=\"\" enclosing=\"\" polygons.=\"\" along=\"\" way,=\"\" open=\"\" problems=\"\" suitable=\"\" for=\"\" graduate=\"\" students=\"\" are=\"\" raised,=\"\" both=\"\" aThe focus of this monograph is converting—reshaping—one 3D convex polyhedron to another via an operation the authors call “tailoring.” A convex polyhedron is a gem-like shape composed of flat facets, the focus of study since Plato and Euclid. The tailoring operation snips off a corner (a “vertex”) of a polyhedron and sutures closed the hole. This is akin to Johannes Kepler’s “vertex truncation,” but differs in that the hole left by a truncated vertex is filled with new surface, whereas tailoring zips the hole closed. A powerful “gluing” theorem of A.D. Alexandrov from 1950 guarantees that, after closing the hole, the result is a new convex polyhedron. Given two convex polyhedra P, and Q inside P, repeated tailoringallows P to be reshaped to Q.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Default Title","offer_id":48858683998443,"sku":"00000_00000_00000_00000","price":238.03,"currency_code":"SGD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0758\/4484\/5803\/files\/9783031475108-1.jpg?v=1781717563","url":"https:\/\/kinokuniya.com.sg\/ja\/products\/9783031475108","provider":"Books Kinokuniya Singapore","version":"1.0","type":"link"}