polytope, orthographic, projections, coxeter, plane, cube, orthoplex, demicube, dimensional, geometry, there, uniform, polytopes, with, symmetry, there, regular, forms, orthoplex, cube, with, vertices, respectively, demicube, added, with, half, symmetry, they,. Orthographic projections in the B7 Coxeter plane 7 cube 7 orthoplex 7 demicube In 7 dimensional geometry there are 128 uniform polytopes with B7 symmetry There are two regular forms the 7 orthoplex and 8 cube with 14 and 128 vertices respectively The 7 demicube is added with half of the symmetry They can be visualized as symmetric orthographic projections in Coxeter planes of the B7 Coxeter group and other subgroups Contents 1 Graphs 2 References Graphs edit Symmetric orthographic projections of these 128 polytopes can be made in the B7 B6 B5 B4 B3 B2 A5 A3 Coxeter planes Ak has k 1 symmetry and Bk has 2k symmetry These 128 polytopes are each shown in these 8 symmetry planes with vertices and edges drawn and vertices colored by the number of overlapping vertices in each projective position Coxeter plane graphs Coxeter Dynkin diagramSchlafli symbolJohnson and Bowers Name B7 14 B6 12 B5 10 B4 8 B3 6 B2 4 A5 6 A3 4 1 3 3 3 3 3 4 7 orthoplexHecatonicosoctaexon zee 2 t1 3 3 3 3 3 4 Rectified 7 orthoplexRectified hecatonicosoctaexon rez 3 t2 3 3 3 3 3 4 Birectified 7 orthoplexBirectified hecatonicosoctaexon barz 4 t3 4 3 3 3 3 3 Trirectified 7 cubeHepteractihecatonicosoctaexon sez 5 t2 4 3 3 3 3 3 Birectified 7 cubeBirectified hepteract bersa 6 t1 4 3 3 3 3 3 Rectified 7 cubeRectified hepteract rasa 7 4 3 3 3 3 3 7 cubeHepteract hept 128 h 4 3 3 3 3 3 7 demicubeHemihepteract 8 t0 1 3 3 3 3 3 4 Truncated 7 orthoplexTruncated hecatonicosoctaexon Taz 9 t0 2 3 3 3 3 3 4 Cantellated 7 orthoplexSmall rhombated hecatonicosoctaexon Sarz 10 t1 2 3 3 3 3 3 4 Bitruncated 7 orthoplexBitruncated hecatonicosoctaexon Botaz 11 t0 3 3 3 3 3 3 4 Runcinated 7 orthoplexSmall prismated hecatonicosoctaexon Spaz 12 t1 3 3 3 3 3 3 4 Bicantellated 7 orthoplexSmall birhombated hecatonicosoctaexon Sebraz 13 t2 3 3 3 3 3 3 4 Tritruncated 7 orthoplexTritruncated hecatonicosoctaexon Totaz 14 t0 4 3 3 3 3 3 4 Stericated 7 orthoplexSmall cellated hecatonicosoctaexon Scaz 15 t1 4 3 3 3 3 3 4 Biruncinated 7 orthoplexSmall biprismated hecatonicosoctaexon Sibpaz 16 t2 4 4 3 3 3 3 3 Tricantellated 7 cubeSmall trirhombi hepteractihecatonicosoctaexon Strasaz 17 t2 3 4 3 3 3 3 3 Tritruncated 7 cubeTritruncated hepteract Tatsa 18 t0 5 3 3 3 3 3 4 Pentellated 7 orthoplexSmall terated hecatonicosoctaexon Staz 19 t1 5 4 3 3 3 3 3 Bistericated 7 cubeSmall bicelli hepteractihecatonicosoctaexon Sabcosaz 20 t1 4 4 3 3 3 3 3 Biruncinated 7 cubeSmall biprismated hepteract Sibposa 21 t1 3 4 3 3 3 3 3 Bicantellated 7 cubeSmall birhombated hepteract Sibrosa 22 t1 2 4 3 3 3 3 3 Bitruncated 7 cubeBitruncated hepteract Betsa 23 t0 6 4 3 3 3 3 3 Hexicated 7 cubeSmall peti hepteractihecatonicosoctaexon Suposaz 24 t0 5 4 3 3 3 3 3 Pentellated 7 cubeSmall terated hepteract Stesa 25 t0 4 4 3 3 3 3 3 Stericated 7 cubeSmall cellated hepteract Scosa 26 t0 3 4 3 3 3 3 3 Runcinated 7 cubeSmall prismated hepteract Spesa 27 t0 2 4 3 3 3 3 3 Cantellated 7 cubeSmall rhombated hepteract Sersa 28 t0 1 4 3 3 3 3 3 Truncated 7 cubeTruncated hepteract Tasa 29 t0 1 2 3 3 3 3 3 4 Cantitruncated 7 orthoplexGreat rhombated hecatonicosoctaexon Garz 30 t0 1 3 3 3 3 3 3 4 Runcitruncated 7 orthoplexPrismatotruncated hecatonicosoctaexon Potaz 31 t0 2 3 3 3 3 3 3 4 Runcicantellated 7 orthoplexPrismatorhombated hecatonicosoctaexon Parz 32 t1 2 3 3 3 3 3 3 4 Bicantitruncated 7 orthoplexGreat birhombated hecatonicosoctaexon Gebraz 33 t0 1 4 3 3 3 3 3 4 Steritruncated 7 orthoplexCellitruncated hecatonicosoctaexon Catz 34 t0 2 4 3 3 3 3 3 4 Stericantellated 7 orthoplexCellirhombated hecatonicosoctaexon Craze 35 t1 2 4 3 3 3 3 3 4 Biruncitruncated 7 orthoplexBiprismatotruncated hecatonicosoctaexon Baptize 36 t0 3 4 3 3 3 3 3 4 Steriruncinated 7 orthoplexCelliprismated hecatonicosoctaexon Copaz 37 t1 3 4 3 3 3 3 3 4 Biruncicantellated 7 orthoplexBiprismatorhombated hecatonicosoctaexon Boparz 38 t2 3 4 4 3 3 3 3 3 Tricantitruncated 7 cubeGreat trirhombi hepteractihecatonicosoctaexon Gotrasaz 39 t0 1 5 3 3 3 3 3 4 Pentitruncated 7 orthoplexTeritruncated hecatonicosoctaexon Tetaz 40 t0 2 5 3 3 3 3 3 4 Penticantellated 7 orthoplexTerirhombated hecatonicosoctaexon Teroz 41 t1 2 5 3 3 3 3 3 4 Bisteritruncated 7 orthoplexBicellitruncated hecatonicosoctaexon Boctaz 42 t0 3 5 3 3 3 3 3 4 Pentiruncinated 7 orthoplexTeriprismated hecatonicosoctaexon Topaz 43 t1 3 5 4 3 3 3 3 3 Bistericantellated 7 cubeBicellirhombi hepteractihecatonicosoctaexon Bacresaz 44 t1 3 4 4 3 3 3 3 3 Biruncicantellated 7 cubeBiprismatorhombated hepteract Bopresa 45 t0 4 5 3 3 3 3 3 4 Pentistericated 7 orthoplexTericellated hecatonicosoctaexon Tocaz 46 t1 2 5 4 3 3 3 3 3 Bisteritruncated 7 cubeBicellitruncated hepteract Bactasa 47 t1 2 4 4 3 3 3 3 3 Biruncitruncated 7 cubeBiprismatotruncated hepteract Biptesa 48 t1 2 3 4 3 3 3 3 3 Bicantitruncated 7 cubeGreat birhombated hepteract Gibrosa 49 t0 1 6 3 3 3 3 3 4 Hexitruncated 7 orthoplexPetitruncated hecatonicosoctaexon Putaz 50 t0 2 6 3 3 3 3 3 4 Hexicantellated 7 orthoplexPetirhombated hecatonicosoctaexon Puraz 51 t0 4 5 4 3 3 3 3 3 Pentistericated 7 cubeTericellated hepteract Tacosa 52 t0 3 6 4 3 3 3 3 3 Hexiruncinated 7 cubePetiprismato hepteractihecatonicosoctaexon Pupsez 53 t0 3 5 4 3 3 3 3 3 Pentiruncinated 7 cubeTeriprismated hepteract Tapsa 54 t0 3 4 4 3 3 3 3 3 Steriruncinated 7 cubeCelliprismated hepteract Capsa 55 t0 2 6 4 3 3 3 3 3 Hexicantellated 7 cubePetirhombated hepteract Purosa 56 t0 2 5 4 3 3 3 3 3 Penticantellated 7 cubeTerirhombated hepteract Tersa 57 t0 2 4 4 3 3 3 3 3 Stericantellated 7 cubeCellirhombated hepteract Carsa 58 t0 2 3 4 3 3 3 3 3 Runcicantellated 7 cubePrismatorhombated hepteract Parsa 59 t0 1 6 4 3 3 3 3 3 Hexitruncated 7 cubePetitruncated hepteract Putsa 60 t0 1 5 4 3 3 3 3 3 Pentitruncated 7 cubeTeritruncated hepteract Tetsa 61 t0 1 4 4 3 3 3 3 3 Steritruncated 7 cubeCellitruncated hepteract Catsa 62 t0 1 3 4 3 3 3 3 3 Runcitruncated 7 cubePrismatotruncated hepteract Petsa 63 t0 1 2 4 3 3 3 3 3 Cantitruncated 7 cubeGreat rhombated hepteract Gersa 64 t0 1 2 3 3 3 3 3 3 4 Runcicantitruncated 7 orthoplexGreat prismated hecatonicosoctaexon Gopaz 65 t0 1 2 4 3 3 3 3 3 4 Stericantitruncated 7 orthoplexCelligreatorhombated hecatonicosoctaexon Cogarz 66 t0 1 3 4 3 3 3 3 3 4 Steriruncitruncated 7 orthoplexCelliprismatotruncated hecatonicosoctaexon Captaz 67 t0 2 3 4 3 3 3 3 3 4 Steriruncicantellated 7 orthoplexCelliprismatorhombated hecatonicosoctaexon Caparz 68 t1 2 3 4 3 3 3 3 3 4 Biruncicantitruncated 7 orthoplexGreat biprismated hecatonicosoctaexon Gibpaz 69 t0 1 2 5 3 3 3 3 3 4 Penticantitruncated 7 orthoplexTerigreatorhombated hecatonicosoctaexon Tograz 70 span, wikipedia, wiki, book, books, library,

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