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