Overview
- Group
- SmallGroup(1152,98791)
- Rank
- 5
- Schläfli Type
- {3,2,24,4}
- Vertices, edges, …
- 3, 3, 24, 48, 4
- Order of s0s1s2s3s4
- 24
- Order of s0s1s2s3s4s3s2s1
- 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
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (2,3);; s1 := (1,2);; s2 := ( 5, 6)( 8, 9)(10,13)(11,15)(12,14)(16,19)(17,21)(18,20)(23,24)(26,27)(28,40)(29,42)(30,41)(31,43)(32,45)(33,44)(34,49)(35,51)(36,50)(37,46)(38,48)(39,47)(53,54)(56,57)(58,61)(59,63)(60,62)(64,67)(65,69)(66,68)(71,72)(74,75)(76,88)(77,90)(78,89)(79,91)(80,93)(81,92)(82,97)(83,99)(84,98)(85,94)(86,96)(87,95);; s3 := ( 4,29)( 5,28)( 6,30)( 7,32)( 8,31)( 9,33)(10,35)(11,34)(12,36)(13,38)(14,37)(15,39)(16,44)(17,43)(18,45)(19,41)(20,40)(21,42)(22,50)(23,49)(24,51)(25,47)(26,46)(27,48)(52,77)(53,76)(54,78)(55,80)(56,79)(57,81)(58,83)(59,82)(60,84)(61,86)(62,85)(63,87)(64,92)(65,91)(66,93)(67,89)(68,88)(69,90)(70,98)(71,97)(72,99)(73,95)(74,94)(75,96);; s4 := ( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,58)(11,59)(12,60)(13,61)(14,62)(15,63)(16,67)(17,68)(18,69)(19,64)(20,65)(21,66)(22,73)(23,74)(24,75)(25,70)(26,71)(27,72)(28,82)(29,83)(30,84)(31,85)(32,86)(33,87)(34,76)(35,77)(36,78)(37,79)(38,80)(39,81)(40,97)(41,98)(42,99)(43,94)(44,95)(45,96)(46,91)(47,92)(48,93)(49,88)(50,89)(51,90);; 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*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s4*s3*s4*s3*s2*s3*s2*s4*s3*s4*s3*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s4*s3*s2*s3*s2*s4*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(99)!(2,3); s1 := Sym(99)!(1,2); s2 := Sym(99)!( 5, 6)( 8, 9)(10,13)(11,15)(12,14)(16,19)(17,21)(18,20)(23,24)(26,27)(28,40)(29,42)(30,41)(31,43)(32,45)(33,44)(34,49)(35,51)(36,50)(37,46)(38,48)(39,47)(53,54)(56,57)(58,61)(59,63)(60,62)(64,67)(65,69)(66,68)(71,72)(74,75)(76,88)(77,90)(78,89)(79,91)(80,93)(81,92)(82,97)(83,99)(84,98)(85,94)(86,96)(87,95); s3 := Sym(99)!( 4,29)( 5,28)( 6,30)( 7,32)( 8,31)( 9,33)(10,35)(11,34)(12,36)(13,38)(14,37)(15,39)(16,44)(17,43)(18,45)(19,41)(20,40)(21,42)(22,50)(23,49)(24,51)(25,47)(26,46)(27,48)(52,77)(53,76)(54,78)(55,80)(56,79)(57,81)(58,83)(59,82)(60,84)(61,86)(62,85)(63,87)(64,92)(65,91)(66,93)(67,89)(68,88)(69,90)(70,98)(71,97)(72,99)(73,95)(74,94)(75,96); s4 := Sym(99)!( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,58)(11,59)(12,60)(13,61)(14,62)(15,63)(16,67)(17,68)(18,69)(19,64)(20,65)(21,66)(22,73)(23,74)(24,75)(25,70)(26,71)(27,72)(28,82)(29,83)(30,84)(31,85)(32,86)(33,87)(34,76)(35,77)(36,78)(37,79)(38,80)(39,81)(40,97)(41,98)(42,99)(43,94)(44,95)(45,96)(46,91)(47,92)(48,93)(49,88)(50,89)(51,90); poly := sub<Sym(99)|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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4, s2*s4*s3*s4*s3*s2*s3*s2*s4*s3*s4*s3*s2*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s4*s3*s2*s3*s2*s4*s3*s2*s3*s2*s3 >;