Overview
- Group
- SmallGroup(1408,19224)
- Rank
- 5
- Schläfli Type
- {2,22,8,2}
- Vertices, edges, …
- 2, 22, 88, 8, 2
- Order of s0s1s2s3s4
- 88
- 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
4-fold
8-fold
11-fold
22-fold
44-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4,13)( 5,12)( 6,11)( 7,10)( 8, 9)(15,24)(16,23)(17,22)(18,21)(19,20)(26,35)(27,34)(28,33)(29,32)(30,31)(37,46)(38,45)(39,44)(40,43)(41,42)(48,57)(49,56)(50,55)(51,54)(52,53)(59,68)(60,67)(61,66)(62,65)(63,64)(70,79)(71,78)(72,77)(73,76)(74,75)(81,90)(82,89)(83,88)(84,87)(85,86);; s2 := ( 3, 4)( 5,13)( 6,12)( 7,11)( 8,10)(14,15)(16,24)(17,23)(18,22)(19,21)(25,37)(26,36)(27,46)(28,45)(29,44)(30,43)(31,42)(32,41)(33,40)(34,39)(35,38)(47,70)(48,69)(49,79)(50,78)(51,77)(52,76)(53,75)(54,74)(55,73)(56,72)(57,71)(58,81)(59,80)(60,90)(61,89)(62,88)(63,87)(64,86)(65,85)(66,84)(67,83)(68,82);; s3 := ( 3,47)( 4,48)( 5,49)( 6,50)( 7,51)( 8,52)( 9,53)(10,54)(11,55)(12,56)(13,57)(14,58)(15,59)(16,60)(17,61)(18,62)(19,63)(20,64)(21,65)(22,66)(23,67)(24,68)(25,80)(26,81)(27,82)(28,83)(29,84)(30,85)(31,86)(32,87)(33,88)(34,89)(35,90)(36,69)(37,70)(38,71)(39,72)(40,73)(41,74)(42,75)(43,76)(44,77)(45,78)(46,79);; s4 := (91,92);; 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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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(92)!(1,2); s1 := Sym(92)!( 4,13)( 5,12)( 6,11)( 7,10)( 8, 9)(15,24)(16,23)(17,22)(18,21)(19,20)(26,35)(27,34)(28,33)(29,32)(30,31)(37,46)(38,45)(39,44)(40,43)(41,42)(48,57)(49,56)(50,55)(51,54)(52,53)(59,68)(60,67)(61,66)(62,65)(63,64)(70,79)(71,78)(72,77)(73,76)(74,75)(81,90)(82,89)(83,88)(84,87)(85,86); s2 := Sym(92)!( 3, 4)( 5,13)( 6,12)( 7,11)( 8,10)(14,15)(16,24)(17,23)(18,22)(19,21)(25,37)(26,36)(27,46)(28,45)(29,44)(30,43)(31,42)(32,41)(33,40)(34,39)(35,38)(47,70)(48,69)(49,79)(50,78)(51,77)(52,76)(53,75)(54,74)(55,73)(56,72)(57,71)(58,81)(59,80)(60,90)(61,89)(62,88)(63,87)(64,86)(65,85)(66,84)(67,83)(68,82); s3 := Sym(92)!( 3,47)( 4,48)( 5,49)( 6,50)( 7,51)( 8,52)( 9,53)(10,54)(11,55)(12,56)(13,57)(14,58)(15,59)(16,60)(17,61)(18,62)(19,63)(20,64)(21,65)(22,66)(23,67)(24,68)(25,80)(26,81)(27,82)(28,83)(29,84)(30,85)(31,86)(32,87)(33,88)(34,89)(35,90)(36,69)(37,70)(38,71)(39,72)(40,73)(41,74)(42,75)(43,76)(44,77)(45,78)(46,79); s4 := Sym(92)!(91,92); poly := sub<Sym(92)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 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 >;