Overview
- Group
- SmallGroup(768,1089270)
- Rank
- 4
- Schläfli Type
- {2,6,24}
- Vertices, edges, …
- 2, 8, 96, 32
- Order of s0s1s2s3
- 8
- 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
4-fold
8-fold
12-fold
16-fold
24-fold
48-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(16,17)(19,23)(20,25)(21,24)(22,26)(28,29)(31,35)(32,37)(33,36)(34,38)(40,41)(43,47)(44,49)(45,48)(46,50)(52,53)(55,59)(56,61)(57,60)(58,62)(64,65)(67,71)(68,73)(69,72)(70,74)(76,77)(79,83)(80,85)(81,84)(82,86)(88,89)(91,95)(92,97)(93,96)(94,98);; s2 := ( 3, 7)( 4, 8)( 5,10)( 6, 9)(13,14)(15,19)(16,20)(17,22)(18,21)(25,26)(27,43)(28,44)(29,46)(30,45)(31,39)(32,40)(33,42)(34,41)(35,47)(36,48)(37,50)(38,49)(51,79)(52,80)(53,82)(54,81)(55,75)(56,76)(57,78)(58,77)(59,83)(60,84)(61,86)(62,85)(63,91)(64,92)(65,94)(66,93)(67,87)(68,88)(69,90)(70,89)(71,95)(72,96)(73,98)(74,97);; s3 := ( 3,54)( 4,52)( 5,53)( 6,51)( 7,62)( 8,60)( 9,61)(10,59)(11,58)(12,56)(13,57)(14,55)(15,66)(16,64)(17,65)(18,63)(19,74)(20,72)(21,73)(22,71)(23,70)(24,68)(25,69)(26,67)(27,90)(28,88)(29,89)(30,87)(31,98)(32,96)(33,97)(34,95)(35,94)(36,92)(37,93)(38,91)(39,78)(40,76)(41,77)(42,75)(43,86)(44,84)(45,85)(46,83)(47,82)(48,80)(49,81)(50,79);; 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*s1*s2,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(98)!(1,2); s1 := Sym(98)!( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(16,17)(19,23)(20,25)(21,24)(22,26)(28,29)(31,35)(32,37)(33,36)(34,38)(40,41)(43,47)(44,49)(45,48)(46,50)(52,53)(55,59)(56,61)(57,60)(58,62)(64,65)(67,71)(68,73)(69,72)(70,74)(76,77)(79,83)(80,85)(81,84)(82,86)(88,89)(91,95)(92,97)(93,96)(94,98); s2 := Sym(98)!( 3, 7)( 4, 8)( 5,10)( 6, 9)(13,14)(15,19)(16,20)(17,22)(18,21)(25,26)(27,43)(28,44)(29,46)(30,45)(31,39)(32,40)(33,42)(34,41)(35,47)(36,48)(37,50)(38,49)(51,79)(52,80)(53,82)(54,81)(55,75)(56,76)(57,78)(58,77)(59,83)(60,84)(61,86)(62,85)(63,91)(64,92)(65,94)(66,93)(67,87)(68,88)(69,90)(70,89)(71,95)(72,96)(73,98)(74,97); s3 := Sym(98)!( 3,54)( 4,52)( 5,53)( 6,51)( 7,62)( 8,60)( 9,61)(10,59)(11,58)(12,56)(13,57)(14,55)(15,66)(16,64)(17,65)(18,63)(19,74)(20,72)(21,73)(22,71)(23,70)(24,68)(25,69)(26,67)(27,90)(28,88)(29,89)(30,87)(31,98)(32,96)(33,97)(34,95)(35,94)(36,92)(37,93)(38,91)(39,78)(40,76)(41,77)(42,75)(43,86)(44,84)(45,85)(46,83)(47,82)(48,80)(49,81)(50,79); 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*s1*s2, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2 >;