Overview
- Group
- SmallGroup(768,323570)
- Rank
- 4
- Schläfli Type
- {2,4,24}
- Vertices, edges, …
- 2, 8, 96, 48
- Order of s0s1s2s3
- 12
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
8-fold
12-fold
16-fold
24-fold
32-fold
48-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 3,27)( 4,28)( 5,29)( 6,30)( 7,31)( 8,32)( 9,33)(10,34)(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)(25,49)(26,50)(51,75)(52,76)(53,77)(54,78)(55,79)(56,80)(57,81)(58,82)(59,83)(60,84)(61,85)(62,86)(63,87)(64,88)(65,89)(66,90)(67,91)(68,92)(69,93)(70,94)(71,95)(72,96)(73,97)(74,98);; s2 := ( 4, 5)( 7, 8)( 9,12)(10,14)(11,13)(16,17)(19,20)(21,24)(22,26)(23,25)(27,39)(28,41)(29,40)(30,42)(31,44)(32,43)(33,48)(34,50)(35,49)(36,45)(37,47)(38,46)(52,53)(55,56)(57,60)(58,62)(59,61)(64,65)(67,68)(69,72)(70,74)(71,73)(75,87)(76,89)(77,88)(78,90)(79,92)(80,91)(81,96)(82,98)(83,97)(84,93)(85,95)(86,94);; s3 := ( 3,76)( 4,75)( 5,77)( 6,79)( 7,78)( 8,80)( 9,82)(10,81)(11,83)(12,85)(13,84)(14,86)(15,97)(16,96)(17,98)(18,94)(19,93)(20,95)(21,91)(22,90)(23,92)(24,88)(25,87)(26,89)(27,52)(28,51)(29,53)(30,55)(31,54)(32,56)(33,58)(34,57)(35,59)(36,61)(37,60)(38,62)(39,73)(40,72)(41,74)(42,70)(43,69)(44,71)(45,67)(46,66)(47,68)(48,64)(49,63)(50,65);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2,
s3*s2*s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s1*s3*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(98)!(1,2); s1 := Sym(98)!( 3,27)( 4,28)( 5,29)( 6,30)( 7,31)( 8,32)( 9,33)(10,34)(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)(25,49)(26,50)(51,75)(52,76)(53,77)(54,78)(55,79)(56,80)(57,81)(58,82)(59,83)(60,84)(61,85)(62,86)(63,87)(64,88)(65,89)(66,90)(67,91)(68,92)(69,93)(70,94)(71,95)(72,96)(73,97)(74,98); s2 := Sym(98)!( 4, 5)( 7, 8)( 9,12)(10,14)(11,13)(16,17)(19,20)(21,24)(22,26)(23,25)(27,39)(28,41)(29,40)(30,42)(31,44)(32,43)(33,48)(34,50)(35,49)(36,45)(37,47)(38,46)(52,53)(55,56)(57,60)(58,62)(59,61)(64,65)(67,68)(69,72)(70,74)(71,73)(75,87)(76,89)(77,88)(78,90)(79,92)(80,91)(81,96)(82,98)(83,97)(84,93)(85,95)(86,94); s3 := Sym(98)!( 3,76)( 4,75)( 5,77)( 6,79)( 7,78)( 8,80)( 9,82)(10,81)(11,83)(12,85)(13,84)(14,86)(15,97)(16,96)(17,98)(18,94)(19,93)(20,95)(21,91)(22,90)(23,92)(24,88)(25,87)(26,89)(27,52)(28,51)(29,53)(30,55)(31,54)(32,56)(33,58)(34,57)(35,59)(36,61)(37,60)(38,62)(39,73)(40,72)(41,74)(42,70)(43,69)(44,71)(45,67)(46,66)(47,68)(48,64)(49,63)(50,65); poly := sub<Sym(98)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2, s3*s2*s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s1*s3*s2*s1 >;