LEADER 03619nam 22006612 450 001 9910450540303321 005 20151005020623.0 010 $a1-316-08575-9 010 $a0-511-54668-8 010 $a1-280-41990-3 010 $a9786610419906 010 $a0-511-16958-2 010 $a1-139-14822-2 010 $a0-511-06500-0 010 $a0-511-05867-5 010 $a0-511-30843-4 010 $a0-511-07346-1 035 $a(CKB)1000000000018102 035 $a(EBL)218008 035 $a(OCoLC)171121086 035 $a(SSID)ssj0000096286 035 $a(PQKBManifestationID)11122289 035 $a(PQKBTitleCode)TC0000096286 035 $a(PQKBWorkID)10076029 035 $a(PQKB)10449392 035 $a(UkCbUP)CR9780511546686 035 $a(MiAaPQ)EBC218008 035 $a(Au-PeEL)EBL218008 035 $a(CaPaEBR)ebr10070348 035 $a(CaONFJC)MIL41990 035 $a(EXLCZ)991000000000018102 100 $a20090508d2002|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAbstract regular polytopes /$fPeter McMullen, Egon Schulte$b[electronic resource] 210 1$aCambridge :$cCambridge University Press,$d2002. 215 $a1 online resource (xiii, 551 pages) $cdigital, PDF file(s) 225 1 $aEncyclopedia of mathematics and its applications ;$vvolume 92 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 311 $a0-521-81496-0 320 $aIncludes bibliographical references (p. 519-538) and indexes. 327 $g1.$tClassical Regular Polytopes --$g2.$tRegular Polytopes --$g3.$tCoxeter Groups --$g4.$tAmalgamation --$g5.$tRealizations --$g6.$tRegular Polytopes on Space-Forms --$g7.$tMixing --$g8.$tTwisting --$g9.$tUnitary Groups and Hermitian Forms --$g10.$tLocally Toroidal 4-Polytopes: I --$g11.$tLocally Toroidal 4-Polytopes: II --$g12.$tHigher Toroidal Polytopes --$g13.$tRegular Polytopes Related to Linear Groups --$g14.$tMiscellaneous Classes of Regular Polytopes. 330 $aAbstract regular polytopes stand at the end of more than two millennia of geometrical research, which began with regular polygons and polyhedra. They are highly symmetric combinatorial structures with distinctive geometric, algebraic or topological properties; in many ways more fascinating than traditional regular polytopes and tessellations. The rapid development of the subject in the past 20 years has resulted in a rich new theory, featuring an attractive interplay of mathematical areas, including geometry, combinatorics, group theory and topology. Abstract regular polytopes and their groups provide an appealing new approach to understanding geometric and combinatorial symmetry. This is the first comprehensive up-to-date account of the subject and its ramifications, and meets a critical need for such a text, because no book has been published in this area of classical and modern discrete geometry since Coxeter's Regular Polytopes (1948) and Regular Complex Polytopes (1974). The book should be of interest to researchers and graduate students in discrete geometry, combinatorics and group theory. 410 0$aEncyclopedia of mathematics and its applications ;$vv. 92. 606 $aPolytopes 615 0$aPolytopes. 676 $a516.3/5 700 $aMcMullen$b Peter$f1942-$055802 702 $aSchulte$b Egon$f1955- 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910450540303321 996 $aAbstract regular polytopes$92489410 997 $aUNINA