Orthogonal projections in B4 Coxeter plane 7-cube Hexicated 7-cube Hexitruncated 7-cube Hexicantellated 7-cube Hexiruncinated 7-cube Hexicantitruncated 7-cube Hexiruncitruncated 7-cube Hexiruncicantellated 7-cube Hexisteritruncated 7-cube Hexistericantellated 7-cube Hexipentitruncated 7-cube Hexiruncicantitruncated 7-cube Hexistericantitruncated 7-cube Hexisteriruncitruncated 7-cube Hexisteriruncicantellated 7-cube Hexipenticantitruncated 7-cube Hexipentiruncitruncated 7-cube Hexisteriruncicantitruncated 7-cube Hexipentiruncicantitruncated 7-cube Hexipentistericantitruncated 7-cube Hexipentisteriruncicantitruncated 7-cube
In seven-dimensional geometry , a hexicated 7-cube is a convex uniform 7-polytope , including 6th-order truncations (hexication) from the regular 7-cube .
There are 32 hexications for the 7-cube, including all permutations of truncations, cantellations, runcinations, sterications, and pentellations. 20 are represented here, while 12 are more easily constructed from the 7-orthoplex .
The simple hexicated 7-cube is also called an expanded 7-cube , with only the first and last nodes ringed, is constructed by an expansion operation applied to the regular 7-cube . The highest form, the hexipentisteriruncicantitruncated 7-cube is more simply called a omnitruncated 7-cube with all of the nodes ringed.
These polytope are among a family of 127 uniform 7-polytopes with B7 symmetry.
Hexicated 7-cube Edit In seven-dimensional geometry , a hexicated 7-cube is a convex uniform 7-polytope , a hexication (6th order truncation) of the regular 7-cube , or alternately can be seen as an expansion operation.
Alternate names Edit Small petated hepteract (acronym: ) (Jonathan Bowers) Images Edit Hexitruncated 7-cube Edit Alternate names Edit Petitruncated hepteract (acronym: ) (Jonathan Bowers) Images Edit Hexicantellated 7-cube Edit Alternate names Edit Petirhombated hepteract (acronym: ) (Jonathan Bowers) Images Edit Hexiruncinated 7-cube Edit Alternate names Edit Petiprismated hepteract (acronym: ) (Jonathan Bowers) Images Edit Hexicantitruncated 7-cube Edit Alternate names Edit Petigreatorhombated hepteract (acronym: ) (Jonathan Bowers) Images Edit Hexiruncitruncated 7-cube Edit Alternate names Edit Petiprismatotruncated hepteract (acronym: ) (Jonathan Bowers) Images Edit Hexiruncicantellated 7-cube Edit In seven-dimensional geometry , a hexiruncicantellated 7-cube is a uniform 7-polytope .
Alternate names Edit Petiprismatorhombated hepteract (acronym: ) (Jonathan Bowers) Images Edit Hexisteritruncated 7-cube Edit Alternate names Edit Peticellitruncated hepteract (acronym: ) (Jonathan Bowers) Images Edit Hexistericantellated 7-cube Edit Alternate names Edit Peticellirhombihepteract (acronym: ) (Jonathan Bowers) Images Edit Hexipentitruncated 7-cube Edit Alternate names Edit Petiteritruncated hepteract (acronym: ) (Jonathan Bowers) Images Edit Hexiruncicantitruncated 7-cube Edit Alternate names Edit Petigreatoprismated hepteract (acronym: ) (Jonathan Bowers) Images Edit Hexistericantitruncated 7-cube Edit Alternate names Edit Peticelligreatorhombated hepteract (acronym: ) (Jonathan Bowers) Images Edit Hexisteriruncitruncated 7-cube Edit Alternate names Edit Peticelliprismatotruncated hepteract (acronym: ) (Jonathan Bowers) Images Edit Hexisteriruncicantellated 7-cube Edit Alternate names Edit Peticelliprismatorhombihepteract (acronym: ) (Jonathan Bowers) Images Edit Hexipenticantitruncated 7-cube Edit Alternate names Edit Petiterigreatorhombated hepteract (acronym: ) (Jonathan Bowers) Images Edit Hexipentiruncitruncated 7-cube Edit Alternate names Edit Great petacellated hepteract (acronym: ) (Jonathan Bowers) Images Edit Hexisteriruncicantitruncated 7-cube Edit Alternate names Edit Great petacellated hepteract (acronym: ) (Jonathan Bowers) Images Edit Hexipentiruncicantitruncated 7-cube Edit Alternate names Edit Petiterigreatoprismated hepteract (acronym: ) (Jonathan Bowers) Images Edit Hexipentistericantitruncated 7-cube Edit Alternate names Edit Petitericelligreatorhombihepteract (acronym: putcagroh) (Jonathan Bowers) Images Edit Omnitruncated 7-cube Edit The omnitruncated 7-cube is the largest uniform 7-polytope in the B7 symmetry of the regular 7-cube. It can also be called the hexipentisteriruncicantitruncated 7-cube which is the long name for the omnitruncation for 7 dimensions, with all reflective mirrors active.
Alternate names Edit Great petated hepteract (Acronym: ) (Jonathan Bowers) Images Edit Notes Edit References Edit H.S.M. Coxeter : H.S.M. Coxeter, Regular Polytopes , 3rd Edition, Dover New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter , edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [1] (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I , [Math. Zeit. 46 (1940) 380-407, MR 2,10] (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II , [Math. Zeit. 188 (1985) 559-591] (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III , [Math. Zeit. 200 (1988) 3-45] Norman Johnson Uniform Polytopes , Manuscript (1991) N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs , PhD (1966) Klitzing, Richard. "7D uniform polytopes (polyexa)". External links Edit Polytopes of Various Dimensions Multi-dimensional Glossary
hexicated, cubes, orthogonal, projections, coxeter, plane7, cube, hexicated, cube, hexitruncated, cube, hexicantellated, cubehexiruncinated, cube, hexicantitruncated, cube, hexiruncitruncated, cube, hexiruncicantellated, cubehexisteritruncated, cube, hexisteri. Orthogonal projections in B4 Coxeter plane7 cube Hexicated 7 cube Hexitruncated 7 cube Hexicantellated 7 cubeHexiruncinated 7 cube Hexicantitruncated 7 cube Hexiruncitruncated 7 cube Hexiruncicantellated 7 cubeHexisteritruncated 7 cube Hexistericantellated 7 cube Hexipentitruncated 7 cube Hexiruncicantitruncated 7 cubeHexistericantitruncated 7 cube Hexisteriruncitruncated 7 cube Hexisteriruncicantellated 7 cube Hexipenticantitruncated 7 cubeHexipentiruncitruncated 7 cube Hexisteriruncicantitruncated 7 cube Hexipentiruncicantitruncated 7 cube Hexipentistericantitruncated 7 cubeHexipentisteriruncicantitruncated 7 cube Omnitruncated 7 cube In seven dimensional geometry a hexicated 7 cube is a convex uniform 7 polytope including 6th order truncations hexication from the regular 7 cube There are 32 hexications for the 7 cube including all permutations of truncations cantellations runcinations sterications and pentellations 20 are represented here while 12 are more easily constructed from the 7 orthoplex The simple hexicated 7 cube is also called an expanded 7 cube with only the first and last nodes ringed is constructed by an expansion operation applied to the regular 7 cube The highest form the hexipentisteriruncicantitruncated 7 cube is more simply called a omnitruncated 7 cube with all of the nodes ringed These polytope are among a family of 127 uniform 7 polytopes with B7 symmetry Contents 1 Hexicated 7 cube 1 1 Alternate names 1 2 Images 2 Hexitruncated 7 cube 2 1 Alternate names 2 2 Images 3 Hexicantellated 7 cube 3 1 Alternate names 3 2 Images 4 Hexiruncinated 7 cube 4 1 Alternate names 4 2 Images 5 Hexicantitruncated 7 cube 5 1 Alternate names 5 2 Images 6 Hexiruncitruncated 7 cube 6 1 Alternate names 6 2 Images 7 Hexiruncicantellated 7 cube 7 1 Alternate names 7 2 Images 8 Hexisteritruncated 7 cube 8 1 Alternate names 8 2 Images 9 Hexistericantellated 7 cube 9 1 Alternate names 9 2 Images 10 Hexipentitruncated 7 cube 10 1 Alternate names 10 2 Images 11 Hexiruncicantitruncated 7 cube 11 1 Alternate names 11 2 Images 12 Hexistericantitruncated 7 cube 12 1 Alternate names 12 2 Images 13 Hexisteriruncitruncated 7 cube 13 1 Alternate names 13 2 Images 14 Hexisteriruncicantellated 7 cube 14 1 Alternate names 14 2 Images 15 Hexipenticantitruncated 7 cube 15 1 Alternate names 15 2 Images 16 Hexipentiruncitruncated 7 cube 16 1 Alternate names 16 2 Images 17 Hexisteriruncicantitruncated 7 cube 17 1 Alternate names 17 2 Images 18 Hexipentiruncicantitruncated 7 cube 18 1 Alternate names 18 2 Images 19 Hexipentistericantitruncated 7 cube 19 1 Alternate names 19 2 Images 20 Omnitruncated 7 cube 20 1 Alternate names 20 2 Images 21 Notes 22 References 23 External linksHexicated 7 cube EditHexicated 7 cubeType uniform 7 polytopeSchlafli symbol t0 6 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces5 faces4 facesCellsFacesEdgesVerticesVertex figureCoxeter groups B7 4 35 Properties convexIn seven dimensional geometry a hexicated 7 cube is a convex uniform 7 polytope a hexication 6th order truncation of the regular 7 cube or alternately can be seen as an expansion operation Alternate names Edit Small petated hepteract acronym Jonathan Bowers Images Edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4Graph nbsp nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3Graph nbsp nbsp Dihedral symmetry 6 4 Hexitruncated 7 cube Edithexitruncated 7 cubeType uniform 7 polytopeSchlafli symbol t0 1 6 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces5 faces4 facesCellsFacesEdgesVerticesVertex figureCoxeter groups B7 4 35 Properties convexAlternate names Edit Petitruncated hepteract acronym Jonathan Bowers Images Edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4Graph nbsp nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3Graph nbsp nbsp Dihedral symmetry 6 4 Hexicantellated 7 cube EditHexicantellated 7 cubeType uniform 7 polytopeSchlafli symbol t0 2 6 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces5 faces4 facesCellsFacesEdgesVerticesVertex figureCoxeter groups B7 4 35 Properties convexAlternate names Edit Petirhombated hepteract acronym Jonathan Bowers Images Edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4Graph nbsp nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3Graph nbsp nbsp Dihedral symmetry 6 4 Hexiruncinated 7 cube EditHexiruncinated 7 cubeType uniform 7 polytopeSchlafli symbol t0 3 6 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces5 faces4 facesCellsFacesEdgesVerticesVertex figureCoxeter groups B7 4 35 Properties convexAlternate names Edit Petiprismated hepteract acronym Jonathan Bowers Images Edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4Graph too complex nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3Graph nbsp nbsp Dihedral symmetry 6 4 Hexicantitruncated 7 cube EditHexicantitruncated 7 cubeType uniform 7 polytopeSchlafli symbol t0 1 2 6 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces5 faces4 facesCellsFacesEdgesVerticesVertex figureCoxeter groups B7 4 35 Properties convexAlternate names Edit Petigreatorhombated hepteract acronym Jonathan Bowers Images Edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4Graph nbsp nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3Graph nbsp nbsp Dihedral symmetry 6 4 Hexiruncitruncated 7 cube EditHexiruncitruncated 7 cubeType uniform 7 polytopeSchlafli symbol t0 1 3 6 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces5 faces4 facesCellsFacesEdgesVerticesVertex figureCoxeter groups B7 4 35 Properties convexAlternate names Edit Petiprismatotruncated hepteract acronym Jonathan Bowers Images Edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4Graph nbsp nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3Graph nbsp nbsp Dihedral symmetry 6 4 Hexiruncicantellated 7 cube EditHexiruncicantellated 7 cubeType uniform 7 polytopeSchlafli symbol t0 2 3 6 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces5 faces4 facesCellsFacesEdgesVerticesVertex figureCoxeter groups B7 4 35 Properties convexIn seven dimensional geometry a hexiruncicantellated 7 cube is a uniform 7 polytope Alternate names Edit Petiprismatorhombated hepteract acronym Jonathan Bowers Images Edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4Graph nbsp nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3Graph nbsp nbsp Dihedral symmetry 6 4 Hexisteritruncated 7 cube Edithexisteritruncated 7 cubeType uniform 7 polytopeSchlafli symbol t0 1 4 6 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces5 faces4 facesCellsFacesEdgesVerticesVertex figureCoxeter groups B7 4 35 Properties convexAlternate names Edit Peticellitruncated hepteract acronym Jonathan Bowers Images Edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4Graph nbsp nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3Graph nbsp nbsp Dihedral symmetry 6 4 Hexistericantellated 7 cube Edithexistericantellated 7 cubeType uniform 7 polytopeSchlafli symbol t0 2 4 6 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces5 faces4 facesCellsFacesEdgesVerticesVertex figureCoxeter groups B7 4 35 Properties convexAlternate names Edit Peticellirhombihepteract acronym Jonathan Bowers Images Edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4Graph nbsp nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3Graph nbsp nbsp Dihedral symmetry 6 4 Hexipentitruncated 7 cube EditHexipentitruncated 7 cubeType uniform 7 polytopeSchlafli symbol t0 1 5 6 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces5 faces4 facesCellsFacesEdgesVerticesVertex figureCoxeter groups B7 4 35 Properties convexAlternate names Edit Petiteritruncated hepteract acronym Jonathan Bowers Images Edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4Graph nbsp nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3Graph nbsp nbsp Dihedral symmetry 6 4 Hexiruncicantitruncated 7 cube EditHexiruncicantitruncated 7 cubeType uniform 7 polytopeSchlafli symbol t0 1 2 3 6 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces5 faces4 facesCellsFacesEdgesVerticesVertex figureCoxeter groups B7 4 35 Properties convexAlternate names Edit Petigreatoprismated hepteract acronym Jonathan Bowers Images Edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4Graph nbsp nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3Graph too complex too complexDihedral symmetry 6 4 Hexistericantitruncated 7 cube EditHexistericantitruncated 7 cubeType uniform 7 polytopeSchlafli symbol t0 1 2 4 6 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces5 faces4 facesCellsFacesEdgesVerticesVertex figureCoxeter groups B7 4 35 Properties convexAlternate names Edit Peticelligreatorhombated hepteract acronym Jonathan Bowers Images Edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4Graph too complex nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3Graph nbsp nbsp Dihedral symmetry 6 4 Hexisteriruncitruncated 7 cube EditHexisteriruncitruncated 7 cubeType uniform 7 polytopeSchlafli symbol t0 1 3 4 6 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces5 faces4 facesCellsFacesEdgesVerticesVertex figureCoxeter groups B7 4 35 Properties convexAlternate names Edit Peticelliprismatotruncated hepteract acronym Jonathan Bowers Images Edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4Graph too complex nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3Graph nbsp nbsp Dihedral symmetry 6 4 Hexisteriruncicantellated 7 cube EditHexisteriruncitruncated 7 cubeType uniform 7 polytopeSchlafli symbol t0 2 3 4 6 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces5 faces4 facesCellsFacesEdgesVerticesVertex figureCoxeter groups B7 4 35 Properties convexAlternate names Edit Peticelliprismatorhombihepteract acronym Jonathan Bowers Images Edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4Graph too complex nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3Graph nbsp nbsp Dihedral symmetry 6 4 Hexipenticantitruncated 7 cube Edithexipenticantitruncated 7 cubeType uniform 7 polytopeSchlafli symbol t0 1 2 5 6 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces5 faces4 facesCellsFacesEdgesVerticesVertex figureCoxeter groups B7 4 35 Properties convexAlternate names Edit Petiterigreatorhombated hepteract acronym Jonathan Bowers Images Edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4Graph nbsp nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3Graph nbsp nbsp Dihedral symmetry 6 4 Hexipentiruncitruncated 7 cube EditHexisteriruncicantitruncated 7 cubeType uniform 7 polytopeSchlafli symbol t0 1 2 3 4 6 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces5 faces4 facesCellsFacesEdgesVerticesVertex figureCoxeter groups B7 4 35 Properties convexAlternate names Edit Great petacellated hepteract acronym Jonathan Bowers Images Edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4Graph too complex nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3Graph nbsp nbsp Dihedral symmetry 6 4 Hexisteriruncicantitruncated 7 cube EditHexisteriruncicantitruncated 7 cubeType uniform 7 polytopeSchlafli symbol t0 1 2 3 4 6 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces5 faces4 facesCellsFacesEdgesVerticesVertex figureCoxeter groups B7 4 35 Properties convexAlternate names Edit Great petacellated hepteract acronym Jonathan Bowers Images Edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4Graph too complex nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3Graph nbsp nbsp Dihedral symmetry 6 4 Hexipentiruncicantitruncated 7 cube EditHexipentiruncicantitruncated 7 cubeType uniform 7 polytopeSchlafli symbol t0 1 2 3 5 6 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces5 faces4 facesCellsFacesEdgesVerticesVertex figureCoxeter groups B7 4 35 Properties convexAlternate names Edit Petiterigreatoprismated hepteract acronym Jonathan Bowers Images Edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4Graph too complex nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3Graph nbsp nbsp Dihedral symmetry 6 4 Hexipentistericantitruncated 7 cube EditHexipentistericantitruncated 7 cubeType uniform 7 polytopeSchlafli symbol t0 1 2 4 5 6 4 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces5 faces4 facesCellsFacesEdgesVerticesVertex figureCoxeter groups B7 4 35 Properties convexAlternate names Edit Petitericelligreatorhombihepteract acronym putcagroh Jonathan Bowers Images Edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4Graph too complex nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3Graph nbsp nbsp Dihedral symmetry 6 4 Omnitruncated 7 cube EditOmnitruncated 7 cubeType uniform 7 polytopeSchlafli symbol t0 1 2 3 4 5 6 36 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 faces5 faces4 facesCellsFacesEdgesVerticesVertex figureCoxeter groups B7 4 35 Properties convexThe omnitruncated 7 cube is the largest uniform 7 polytope in the B7 symmetry of the regular 7 cube It can also be called the hexipentisteriruncicantitruncated 7 cube which is the long name for the omnitruncation for 7 dimensions with all reflective mirrors active Alternate names Edit Great petated hepteract Acronym Jonathan Bowers Images Edit orthographic projections Coxeter plane B7 A6 B6 D7 B5 D6 A4Graph too complex nbsp nbsp Dihedral symmetry 14 12 10 Coxeter plane B4 D5 B3 D4 A2 B2 D3Graph nbsp nbsp nbsp Dihedral symmetry 8 6 4 Coxeter plane A5 A3Graph nbsp nbsp Dihedral symmetry 6 4 Notes EditReferences EditH S M Coxeter H S M Coxeter Regular Polytopes 3rd Edition Dover New York 1973 Kaleidoscopes Selected Writings of H S M Coxeter edited by F Arthur Sherk Peter McMullen Anthony C Thompson Asia Ivic Weiss Wiley Interscience Publication 1995 ISBN 978 0 471 01003 6 1 Paper 22 H S M Coxeter Regular and Semi Regular Polytopes I Math Zeit 46 1940 380 407 MR 2 10 Paper 23 H S M Coxeter Regular and Semi Regular Polytopes II Math Zeit 188 1985 559 591 Paper 24 H S M Coxeter Regular and Semi Regular Polytopes III Math Zeit 200 1988 3 45 Norman Johnson Uniform Polytopes Manuscript 1991 N W Johnson The Theory of Uniform Polytopes and Honeycombs PhD 1966 Klitzing Richard 7D uniform polytopes polyexa x3o3o3o3o3o4x x3x3o3o3o3o3x x3o3o3x3o3o4x x3x3x3o3o3o4x x3x3o3x3o3o4x x3o3x3x3o3o4x x3o3x3o3o3x4x x3o3x3o3x3o4x x3x3o3o3o3x4x x3x3x3x3o3o4x x3x3x3o3x3o4x x3x3o3x3x3o4x x3o3x3x3x3o4x x3x3x3oxo3x4x x3x3x3x3x3o4x x3x3x3o3x3x4x x3x3o3x3x3x4x x3x3x3x3x3x4x External links EditPolytopes of Various Dimensions Multi dimensional GlossaryvteFundamental convex regular and uniform polytopes in dimensions 2 10Family An Bn I2 p Dn E6 E7 E8 F4 G2 HnRegular polygon Triangle Square p gon Hexagon PentagonUniform polyhedron Tetrahedron Octahedron Cube Demicube Dodecahedron IcosahedronUniform polychoron Pentachoron 16 cell Tesseract Demitesseract 24 cell 120 cell 600 cellUniform 5 polytope 5 simplex 5 orthoplex 5 cube 5 demicubeUniform 6 polytope 6 simplex 6 orthoplex 6 cube 6 demicube 122 221Uniform 7 polytope 7 simplex 7 orthoplex 7 cube 7 demicube 132 231 321Uniform 8 polytope 8 simplex 8 orthoplex 8 cube 8 demicube 142 241 421Uniform 9 polytope 9 simplex 9 orthoplex 9 cube 9 demicubeUniform 10 polytope 10 simplex 10 orthoplex 10 cube 10 demicubeUniform n polytope n simplex n orthoplex n cube n demicube 1k2 2k1 k21 n pentagonal polytopeTopics Polytope families Regular polytope List of regular polytopes and compounds Retrieved from https en wikipedia org w index php title Hexicated 7 cubes amp oldid 817107027 Hexicantellated 7 cube, wikipedia, wiki , book, books, library,
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