Overview
- Group
- SmallGroup(768,1089108)
- Rank
- 5
- Schläfli Type
- {2,6,4,4}
- Vertices, edges, …
- 2, 6, 24, 16, 8
- Order of s0s1s2s3s4
- 6
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
2-fold
4-fold
8-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 5, 6)( 7,11)( 8,12)( 9,14)(10,13)(17,18)(19,35)(20,36)(21,38)(22,37)(23,43)(24,44)(25,46)(26,45)(27,39)(28,40)(29,42)(30,41)(31,47)(32,48)(33,50)(34,49)(53,54)(55,59)(56,60)(57,62)(58,61)(65,66)(67,83)(68,84)(69,86)(70,85)(71,91)(72,92)(73,94)(74,93)(75,87)(76,88)(77,90)(78,89)(79,95)(80,96)(81,98)(82,97);; s2 := ( 3,67)( 4,70)( 5,69)( 6,68)( 7,71)( 8,74)( 9,73)(10,72)(11,79)(12,82)(13,81)(14,80)(15,75)(16,78)(17,77)(18,76)(19,51)(20,54)(21,53)(22,52)(23,55)(24,58)(25,57)(26,56)(27,63)(28,66)(29,65)(30,64)(31,59)(32,62)(33,61)(34,60)(35,83)(36,86)(37,85)(38,84)(39,87)(40,90)(41,89)(42,88)(43,95)(44,98)(45,97)(46,96)(47,91)(48,94)(49,93)(50,92);; s3 := ( 3,15)( 4,16)( 5,17)( 6,18)( 7,11)( 8,12)( 9,13)(10,14)(19,31)(20,32)(21,33)(22,34)(23,27)(24,28)(25,29)(26,30)(35,47)(36,48)(37,49)(38,50)(39,43)(40,44)(41,45)(42,46)(51,63)(52,64)(53,65)(54,66)(55,59)(56,60)(57,61)(58,62)(67,79)(68,80)(69,81)(70,82)(71,75)(72,76)(73,77)(74,78)(83,95)(84,96)(85,97)(86,98)(87,91)(88,92)(89,93)(90,94);; s4 := ( 7, 9)( 8,10)(11,14)(12,13)(15,16)(17,18)(23,25)(24,26)(27,30)(28,29)(31,32)(33,34)(39,41)(40,42)(43,46)(44,45)(47,48)(49,50)(55,57)(56,58)(59,62)(60,61)(63,64)(65,66)(71,73)(72,74)(75,78)(76,77)(79,80)(81,82)(87,89)(88,90)(91,94)(92,93)(95,96)(97,98);; poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s2*s3*s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s3*s2*s1*s3*s2*s3*s2*s1*s2, s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(98)!(1,2); s1 := Sym(98)!( 5, 6)( 7,11)( 8,12)( 9,14)(10,13)(17,18)(19,35)(20,36)(21,38)(22,37)(23,43)(24,44)(25,46)(26,45)(27,39)(28,40)(29,42)(30,41)(31,47)(32,48)(33,50)(34,49)(53,54)(55,59)(56,60)(57,62)(58,61)(65,66)(67,83)(68,84)(69,86)(70,85)(71,91)(72,92)(73,94)(74,93)(75,87)(76,88)(77,90)(78,89)(79,95)(80,96)(81,98)(82,97); s2 := Sym(98)!( 3,67)( 4,70)( 5,69)( 6,68)( 7,71)( 8,74)( 9,73)(10,72)(11,79)(12,82)(13,81)(14,80)(15,75)(16,78)(17,77)(18,76)(19,51)(20,54)(21,53)(22,52)(23,55)(24,58)(25,57)(26,56)(27,63)(28,66)(29,65)(30,64)(31,59)(32,62)(33,61)(34,60)(35,83)(36,86)(37,85)(38,84)(39,87)(40,90)(41,89)(42,88)(43,95)(44,98)(45,97)(46,96)(47,91)(48,94)(49,93)(50,92); s3 := Sym(98)!( 3,15)( 4,16)( 5,17)( 6,18)( 7,11)( 8,12)( 9,13)(10,14)(19,31)(20,32)(21,33)(22,34)(23,27)(24,28)(25,29)(26,30)(35,47)(36,48)(37,49)(38,50)(39,43)(40,44)(41,45)(42,46)(51,63)(52,64)(53,65)(54,66)(55,59)(56,60)(57,61)(58,62)(67,79)(68,80)(69,81)(70,82)(71,75)(72,76)(73,77)(74,78)(83,95)(84,96)(85,97)(86,98)(87,91)(88,92)(89,93)(90,94); s4 := Sym(98)!( 7, 9)( 8,10)(11,14)(12,13)(15,16)(17,18)(23,25)(24,26)(27,30)(28,29)(31,32)(33,34)(39,41)(40,42)(43,46)(44,45)(47,48)(49,50)(55,57)(56,58)(59,62)(60,61)(63,64)(65,66)(71,73)(72,74)(75,78)(76,77)(79,80)(81,82)(87,89)(88,90)(91,94)(92,93)(95,96)(97,98); poly := sub<Sym(98)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4, s3*s2*s1*s3*s2*s3*s2*s1*s2, s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;