Overview
- Group
- SmallGroup(768,323570)
- Rank
- 4
- Schläfli Type
- {2,24,4}
- Vertices, edges, …
- 2, 48, 96, 8
- 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 := ( 3,75)( 4,77)( 5,76)( 6,78)( 7,80)( 8,79)( 9,81)(10,83)(11,82)(12,84)(13,86)(14,85)(15,96)(16,98)(17,97)(18,93)(19,95)(20,94)(21,90)(22,92)(23,91)(24,87)(25,89)(26,88)(27,51)(28,53)(29,52)(30,54)(31,56)(32,55)(33,57)(34,59)(35,58)(36,60)(37,62)(38,61)(39,72)(40,74)(41,73)(42,69)(43,71)(44,70)(45,66)(46,68)(47,67)(48,63)(49,65)(50,64);; s2 := ( 3, 4)( 6, 7)( 9,13)(10,12)(11,14)(15,16)(18,19)(21,25)(22,24)(23,26)(27,40)(28,39)(29,41)(30,43)(31,42)(32,44)(33,49)(34,48)(35,50)(36,46)(37,45)(38,47)(51,52)(54,55)(57,61)(58,60)(59,62)(63,64)(66,67)(69,73)(70,72)(71,74)(75,88)(76,87)(77,89)(78,91)(79,90)(80,92)(81,97)(82,96)(83,98)(84,94)(85,93)(86,95);; s3 := ( 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);; 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,
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s3*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,
s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s1*s3*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(98)!(1,2); s1 := Sym(98)!( 3,75)( 4,77)( 5,76)( 6,78)( 7,80)( 8,79)( 9,81)(10,83)(11,82)(12,84)(13,86)(14,85)(15,96)(16,98)(17,97)(18,93)(19,95)(20,94)(21,90)(22,92)(23,91)(24,87)(25,89)(26,88)(27,51)(28,53)(29,52)(30,54)(31,56)(32,55)(33,57)(34,59)(35,58)(36,60)(37,62)(38,61)(39,72)(40,74)(41,73)(42,69)(43,71)(44,70)(45,66)(46,68)(47,67)(48,63)(49,65)(50,64); s2 := Sym(98)!( 3, 4)( 6, 7)( 9,13)(10,12)(11,14)(15,16)(18,19)(21,25)(22,24)(23,26)(27,40)(28,39)(29,41)(30,43)(31,42)(32,44)(33,49)(34,48)(35,50)(36,46)(37,45)(38,47)(51,52)(54,55)(57,61)(58,60)(59,62)(63,64)(66,67)(69,73)(70,72)(71,74)(75,88)(76,87)(77,89)(78,91)(79,90)(80,92)(81,97)(82,96)(83,98)(84,94)(85,93)(86,95); s3 := 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); 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, s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s3*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, s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s1*s3*s2*s1 >;