Polytope of Type {6,22} with group SmallGroup(264,34)

Overview

Group: SmallGroup(264,34)
Rank: 3
Schläfli Type: {6,22}
Vertices, edges, …: 6, 66, 22
Order of s₀s₁s₂: 66
Order of s₀s₁s₂s₁: 2
Also known as: {6,22|2}. if this polytope has another name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

3-fold

{2,22}*88

6-fold

{2,11}*44

11-fold

{6,2}*24

22-fold

{3,2}*12

33-fold

{2,2}*8

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

7-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := (12,23)(13,24)(14,25)(15,26)(16,27)(17,28)(18,29)(19,30)(20,31)(21,32)(22,33)(45,56)(46,57)(47,58)(48,59)(49,60)(50,61)(51,62)(52,63)(53,64)(54,65)(55,66);;
s1 := ( 1,12)( 2,22)( 3,21)( 4,20)( 5,19)( 6,18)( 7,17)( 8,16)( 9,15)(10,14)(11,13)(24,33)(25,32)(26,31)(27,30)(28,29)(34,45)(35,55)(36,54)(37,53)(38,52)(39,51)(40,50)(41,49)(42,48)(43,47)(44,46)(57,66)(58,65)(59,64)(60,63)(61,62);;
s2 := ( 1,35)( 2,34)( 3,44)( 4,43)( 5,42)( 6,41)( 7,40)( 8,39)( 9,38)(10,37)(11,36)(12,46)(13,45)(14,55)(15,54)(16,53)(17,52)(18,51)(19,50)(20,49)(21,48)(22,47)(23,57)(24,56)(25,66)(26,65)(27,64)(28,63)(29,62)(30,61)(31,60)(32,59)(33,58);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, 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 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(66)!(12,23)(13,24)(14,25)(15,26)(16,27)(17,28)(18,29)(19,30)(20,31)(21,32)(22,33)(45,56)(46,57)(47,58)(48,59)(49,60)(50,61)(51,62)(52,63)(53,64)(54,65)(55,66);
s1 := Sym(66)!( 1,12)( 2,22)( 3,21)( 4,20)( 5,19)( 6,18)( 7,17)( 8,16)( 9,15)(10,14)(11,13)(24,33)(25,32)(26,31)(27,30)(28,29)(34,45)(35,55)(36,54)(37,53)(38,52)(39,51)(40,50)(41,49)(42,48)(43,47)(44,46)(57,66)(58,65)(59,64)(60,63)(61,62);
s2 := Sym(66)!( 1,35)( 2,34)( 3,44)( 4,43)( 5,42)( 6,41)( 7,40)( 8,39)( 9,38)(10,37)(11,36)(12,46)(13,45)(14,55)(15,54)(16,53)(17,52)(18,51)(19,50)(20,49)(21,48)(22,47)(23,57)(24,56)(25,66)(26,65)(27,64)(28,63)(29,62)(30,61)(31,60)(32,59)(33,58);
poly := sub<Sym(66)|s0,s1,s2>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, 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 >;

References