Overview
- Group
- SmallGroup(1344,11516)
- Rank
- 5
- Schläfli Type
- {2,2,12,14}
- Vertices, edges, …
- 2, 2, 12, 84, 14
- 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)(47,68)(48,69)(49,70)(50,71)(51,72)(52,73)(53,74)(54,82)(55,83)(56,84)(57,85)(58,86)(59,87)(60,88)(61,75)(62,76)(63,77)(64,78)(65,79)(66,80)(67,81);; s3 := ( 5,54)( 6,60)( 7,59)( 8,58)( 9,57)(10,56)(11,55)(12,47)(13,53)(14,52)(15,51)(16,50)(17,49)(18,48)(19,61)(20,67)(21,66)(22,65)(23,64)(24,63)(25,62)(26,75)(27,81)(28,80)(29,79)(30,78)(31,77)(32,76)(33,68)(34,74)(35,73)(36,72)(37,71)(38,70)(39,69)(40,82)(41,88)(42,87)(43,86)(44,85)(45,84)(46,83);; s4 := ( 5, 6)( 7,11)( 8,10)(12,13)(14,18)(15,17)(19,20)(21,25)(22,24)(26,27)(28,32)(29,31)(33,34)(35,39)(36,38)(40,41)(42,46)(43,45)(47,48)(49,53)(50,52)(54,55)(56,60)(57,59)(61,62)(63,67)(64,66)(68,69)(70,74)(71,73)(75,76)(77,81)(78,80)(82,83)(84,88)(85,87);; 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*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 ];;
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)(47,68)(48,69)(49,70)(50,71)(51,72)(52,73)(53,74)(54,82)(55,83)(56,84)(57,85)(58,86)(59,87)(60,88)(61,75)(62,76)(63,77)(64,78)(65,79)(66,80)(67,81); s3 := Sym(88)!( 5,54)( 6,60)( 7,59)( 8,58)( 9,57)(10,56)(11,55)(12,47)(13,53)(14,52)(15,51)(16,50)(17,49)(18,48)(19,61)(20,67)(21,66)(22,65)(23,64)(24,63)(25,62)(26,75)(27,81)(28,80)(29,79)(30,78)(31,77)(32,76)(33,68)(34,74)(35,73)(36,72)(37,71)(38,70)(39,69)(40,82)(41,88)(42,87)(43,86)(44,85)(45,84)(46,83); s4 := Sym(88)!( 5, 6)( 7,11)( 8,10)(12,13)(14,18)(15,17)(19,20)(21,25)(22,24)(26,27)(28,32)(29,31)(33,34)(35,39)(36,38)(40,41)(42,46)(43,45)(47,48)(49,53)(50,52)(54,55)(56,60)(57,59)(61,62)(63,67)(64,66)(68,69)(70,74)(71,73)(75,76)(77,81)(78,80)(82,83)(84,88)(85,87); 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*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 >;