Overview
- Group
- SmallGroup(1344,11517)
- Rank
- 5
- Schläfli Type
- {2,2,6,28}
- Vertices, edges, …
- 2, 2, 6, 84, 28
- 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 := (1,2);; s1 := (3,4);; s2 := (12,19)(13,20)(14,21)(15,22)(16,23)(17,24)(18,25)(33,40)(34,41)(35,42)(36,43)(37,44)(38,45)(39,46)(54,61)(55,62)(56,63)(57,64)(58,65)(59,66)(60,67)(75,82)(76,83)(77,84)(78,85)(79,86)(80,87)(81,88);; s3 := ( 5,12)( 6,18)( 7,17)( 8,16)( 9,15)(10,14)(11,13)(20,25)(21,24)(22,23)(26,33)(27,39)(28,38)(29,37)(30,36)(31,35)(32,34)(41,46)(42,45)(43,44)(47,75)(48,81)(49,80)(50,79)(51,78)(52,77)(53,76)(54,68)(55,74)(56,73)(57,72)(58,71)(59,70)(60,69)(61,82)(62,88)(63,87)(64,86)(65,85)(66,84)(67,83);; s4 := ( 5,48)( 6,47)( 7,53)( 8,52)( 9,51)(10,50)(11,49)(12,55)(13,54)(14,60)(15,59)(16,58)(17,57)(18,56)(19,62)(20,61)(21,67)(22,66)(23,65)(24,64)(25,63)(26,69)(27,68)(28,74)(29,73)(30,72)(31,71)(32,70)(33,76)(34,75)(35,81)(36,80)(37,79)(38,78)(39,77)(40,83)(41,82)(42,88)(43,87)(44,86)(45,85)(46,84);; 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,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(88)!(1,2); s1 := Sym(88)!(3,4); s2 := Sym(88)!(12,19)(13,20)(14,21)(15,22)(16,23)(17,24)(18,25)(33,40)(34,41)(35,42)(36,43)(37,44)(38,45)(39,46)(54,61)(55,62)(56,63)(57,64)(58,65)(59,66)(60,67)(75,82)(76,83)(77,84)(78,85)(79,86)(80,87)(81,88); s3 := Sym(88)!( 5,12)( 6,18)( 7,17)( 8,16)( 9,15)(10,14)(11,13)(20,25)(21,24)(22,23)(26,33)(27,39)(28,38)(29,37)(30,36)(31,35)(32,34)(41,46)(42,45)(43,44)(47,75)(48,81)(49,80)(50,79)(51,78)(52,77)(53,76)(54,68)(55,74)(56,73)(57,72)(58,71)(59,70)(60,69)(61,82)(62,88)(63,87)(64,86)(65,85)(66,84)(67,83); s4 := Sym(88)!( 5,48)( 6,47)( 7,53)( 8,52)( 9,51)(10,50)(11,49)(12,55)(13,54)(14,60)(15,59)(16,58)(17,57)(18,56)(19,62)(20,61)(21,67)(22,66)(23,65)(24,64)(25,63)(26,69)(27,68)(28,74)(29,73)(30,72)(31,71)(32,70)(33,76)(34,75)(35,81)(36,80)(37,79)(38,78)(39,77)(40,83)(41,82)(42,88)(43,87)(44,86)(45,85)(46,84); 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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;