Overview
- Group
- SmallGroup(1344,11517)
- Rank
- 5
- Schläfli Type
- {6,28,2,2}
- Vertices, edges, …
- 6, 84, 28, 2, 2
- Order of s0s1s2s3s4
- 84
- 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
6-fold
7-fold
12-fold
14-fold
21-fold
28-fold
42-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 8,15)( 9,16)(10,17)(11,18)(12,19)(13,20)(14,21)(29,36)(30,37)(31,38)(32,39)(33,40)(34,41)(35,42)(50,57)(51,58)(52,59)(53,60)(54,61)(55,62)(56,63)(71,78)(72,79)(73,80)(74,81)(75,82)(76,83)(77,84);; s1 := ( 1, 8)( 2,14)( 3,13)( 4,12)( 5,11)( 6,10)( 7, 9)(16,21)(17,20)(18,19)(22,29)(23,35)(24,34)(25,33)(26,32)(27,31)(28,30)(37,42)(38,41)(39,40)(43,71)(44,77)(45,76)(46,75)(47,74)(48,73)(49,72)(50,64)(51,70)(52,69)(53,68)(54,67)(55,66)(56,65)(57,78)(58,84)(59,83)(60,82)(61,81)(62,80)(63,79);; s2 := ( 1,44)( 2,43)( 3,49)( 4,48)( 5,47)( 6,46)( 7,45)( 8,51)( 9,50)(10,56)(11,55)(12,54)(13,53)(14,52)(15,58)(16,57)(17,63)(18,62)(19,61)(20,60)(21,59)(22,65)(23,64)(24,70)(25,69)(26,68)(27,67)(28,66)(29,72)(30,71)(31,77)(32,76)(33,75)(34,74)(35,73)(36,79)(37,78)(38,84)(39,83)(40,82)(41,81)(42,80);; s3 := (85,86);; s4 := (87,88);; 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,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s0*s1*s2*s1*s0*s1*s2*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(88)!( 8,15)( 9,16)(10,17)(11,18)(12,19)(13,20)(14,21)(29,36)(30,37)(31,38)(32,39)(33,40)(34,41)(35,42)(50,57)(51,58)(52,59)(53,60)(54,61)(55,62)(56,63)(71,78)(72,79)(73,80)(74,81)(75,82)(76,83)(77,84); s1 := Sym(88)!( 1, 8)( 2,14)( 3,13)( 4,12)( 5,11)( 6,10)( 7, 9)(16,21)(17,20)(18,19)(22,29)(23,35)(24,34)(25,33)(26,32)(27,31)(28,30)(37,42)(38,41)(39,40)(43,71)(44,77)(45,76)(46,75)(47,74)(48,73)(49,72)(50,64)(51,70)(52,69)(53,68)(54,67)(55,66)(56,65)(57,78)(58,84)(59,83)(60,82)(61,81)(62,80)(63,79); s2 := Sym(88)!( 1,44)( 2,43)( 3,49)( 4,48)( 5,47)( 6,46)( 7,45)( 8,51)( 9,50)(10,56)(11,55)(12,54)(13,53)(14,52)(15,58)(16,57)(17,63)(18,62)(19,61)(20,60)(21,59)(22,65)(23,64)(24,70)(25,69)(26,68)(27,67)(28,66)(29,72)(30,71)(31,77)(32,76)(33,75)(34,74)(35,73)(36,79)(37,78)(38,84)(39,83)(40,82)(41,81)(42,80); s3 := Sym(88)!(85,86); s4 := Sym(88)!(87,88); poly := sub<Sym(88)|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, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, s0*s1*s2*s1*s0*s1*s2*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;