Overview
- Group
- SmallGroup(704,1204)
- Rank
- 4
- Schläfli Type
- {8,22,2}
- Vertices, edges, …
- 8, 88, 22, 2
- Order of s0s1s2s3
- 88
- 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
11-fold
22-fold
44-fold
Covers minimal covers in bold
2-fold
Representations
Permutation Representation (GAP)
s0 := (23,34)(24,35)(25,36)(26,37)(27,38)(28,39)(29,40)(30,41)(31,42)(32,43)(33,44)(45,67)(46,68)(47,69)(48,70)(49,71)(50,72)(51,73)(52,74)(53,75)(54,76)(55,77)(56,78)(57,79)(58,80)(59,81)(60,82)(61,83)(62,84)(63,85)(64,86)(65,87)(66,88);; s1 := ( 1,45)( 2,55)( 3,54)( 4,53)( 5,52)( 6,51)( 7,50)( 8,49)( 9,48)(10,47)(11,46)(12,56)(13,66)(14,65)(15,64)(16,63)(17,62)(18,61)(19,60)(20,59)(21,58)(22,57)(23,78)(24,88)(25,87)(26,86)(27,85)(28,84)(29,83)(30,82)(31,81)(32,80)(33,79)(34,67)(35,77)(36,76)(37,75)(38,74)(39,73)(40,72)(41,71)(42,70)(43,69)(44,68);; s2 := ( 1, 2)( 3,11)( 4,10)( 5, 9)( 6, 8)(12,13)(14,22)(15,21)(16,20)(17,19)(23,24)(25,33)(26,32)(27,31)(28,30)(34,35)(36,44)(37,43)(38,42)(39,41)(45,46)(47,55)(48,54)(49,53)(50,52)(56,57)(58,66)(59,65)(60,64)(61,63)(67,68)(69,77)(70,76)(71,75)(72,74)(78,79)(80,88)(81,87)(82,86)(83,85);; s3 := (89,90);; 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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(90)!(23,34)(24,35)(25,36)(26,37)(27,38)(28,39)(29,40)(30,41)(31,42)(32,43)(33,44)(45,67)(46,68)(47,69)(48,70)(49,71)(50,72)(51,73)(52,74)(53,75)(54,76)(55,77)(56,78)(57,79)(58,80)(59,81)(60,82)(61,83)(62,84)(63,85)(64,86)(65,87)(66,88); s1 := Sym(90)!( 1,45)( 2,55)( 3,54)( 4,53)( 5,52)( 6,51)( 7,50)( 8,49)( 9,48)(10,47)(11,46)(12,56)(13,66)(14,65)(15,64)(16,63)(17,62)(18,61)(19,60)(20,59)(21,58)(22,57)(23,78)(24,88)(25,87)(26,86)(27,85)(28,84)(29,83)(30,82)(31,81)(32,80)(33,79)(34,67)(35,77)(36,76)(37,75)(38,74)(39,73)(40,72)(41,71)(42,70)(43,69)(44,68); s2 := Sym(90)!( 1, 2)( 3,11)( 4,10)( 5, 9)( 6, 8)(12,13)(14,22)(15,21)(16,20)(17,19)(23,24)(25,33)(26,32)(27,31)(28,30)(34,35)(36,44)(37,43)(38,42)(39,41)(45,46)(47,55)(48,54)(49,53)(50,52)(56,57)(58,66)(59,65)(60,64)(61,63)(67,68)(69,77)(70,76)(71,75)(72,74)(78,79)(80,88)(81,87)(82,86)(83,85); s3 := Sym(90)!(89,90); poly := sub<Sym(90)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;