Overview
- Group
- SmallGroup(1344,11661)
- Rank
- 5
- Schläfli Type
- {2,2,42,4}
- Vertices, edges, …
- 2, 2, 42, 84, 4
- 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
4-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 := (1,2);; s1 := (3,4);; s2 := ( 6,11)( 7,10)( 8, 9)(12,19)(13,25)(14,24)(15,23)(16,22)(17,21)(18,20)(27,32)(28,31)(29,30)(33,40)(34,46)(35,45)(36,44)(37,43)(38,42)(39,41)(48,53)(49,52)(50,51)(54,61)(55,67)(56,66)(57,65)(58,64)(59,63)(60,62)(69,74)(70,73)(71,72)(75,82)(76,88)(77,87)(78,86)(79,85)(80,84)(81,83);; s3 := ( 5,13)( 6,12)( 7,18)( 8,17)( 9,16)(10,15)(11,14)(19,20)(21,25)(22,24)(26,34)(27,33)(28,39)(29,38)(30,37)(31,36)(32,35)(40,41)(42,46)(43,45)(47,76)(48,75)(49,81)(50,80)(51,79)(52,78)(53,77)(54,69)(55,68)(56,74)(57,73)(58,72)(59,71)(60,70)(61,83)(62,82)(63,88)(64,87)(65,86)(66,85)(67,84);; s4 := ( 5,47)( 6,48)( 7,49)( 8,50)( 9,51)(10,52)(11,53)(12,54)(13,55)(14,56)(15,57)(16,58)(17,59)(18,60)(19,61)(20,62)(21,63)(22,64)(23,65)(24,66)(25,67)(26,68)(27,69)(28,70)(29,71)(30,72)(31,73)(32,74)(33,75)(34,76)(35,77)(36,78)(37,79)(38,80)(39,81)(40,82)(41,83)(42,84)(43,85)(44,86)(45,87)(46,88);; 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*s1*s0*s1,
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, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(88)!(1,2); s1 := Sym(88)!(3,4); s2 := Sym(88)!( 6,11)( 7,10)( 8, 9)(12,19)(13,25)(14,24)(15,23)(16,22)(17,21)(18,20)(27,32)(28,31)(29,30)(33,40)(34,46)(35,45)(36,44)(37,43)(38,42)(39,41)(48,53)(49,52)(50,51)(54,61)(55,67)(56,66)(57,65)(58,64)(59,63)(60,62)(69,74)(70,73)(71,72)(75,82)(76,88)(77,87)(78,86)(79,85)(80,84)(81,83); s3 := Sym(88)!( 5,13)( 6,12)( 7,18)( 8,17)( 9,16)(10,15)(11,14)(19,20)(21,25)(22,24)(26,34)(27,33)(28,39)(29,38)(30,37)(31,36)(32,35)(40,41)(42,46)(43,45)(47,76)(48,75)(49,81)(50,80)(51,79)(52,78)(53,77)(54,69)(55,68)(56,74)(57,73)(58,72)(59,71)(60,70)(61,83)(62,82)(63,88)(64,87)(65,86)(66,85)(67,84); s4 := Sym(88)!( 5,47)( 6,48)( 7,49)( 8,50)( 9,51)(10,52)(11,53)(12,54)(13,55)(14,56)(15,57)(16,58)(17,59)(18,60)(19,61)(20,62)(21,63)(22,64)(23,65)(24,66)(25,67)(26,68)(27,69)(28,70)(29,71)(30,72)(31,73)(32,74)(33,75)(34,76)(35,77)(36,78)(37,79)(38,80)(39,81)(40,82)(41,83)(42,84)(43,85)(44,86)(45,87)(46,88); 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*s1*s0*s1, 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, s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;