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Polytope of Type {6,22}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,22}*264
Also Known As : {6,22|2}. if this polytope has another name.
Group : SmallGroup(264,34)
Rank : 3
Schlafli Type : {6,22}
Number of vertices, edges, etc : 6, 66, 22
Order of s0s1s2 : 66
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,22,2} of size 528
   {6,22,4} of size 1056
   {6,22,6} of size 1584
Vertex Figure Of :
   {2,6,22} of size 528
   {3,6,22} of size 792
   {4,6,22} of size 1056
   {3,6,22} of size 1056
   {4,6,22} of size 1056
   {6,6,22} of size 1584
   {6,6,22} of size 1584
   {6,6,22} of size 1584
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,22}*88
   6-fold quotients : {2,11}*44
   11-fold quotients : {6,2}*24
   22-fold quotients : {3,2}*12
   33-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,22}*528, {6,44}*528a
   3-fold covers : {18,22}*792, {6,66}*792a, {6,66}*792b
   4-fold covers : {24,22}*1056, {6,88}*1056, {12,44}*1056, {6,44}*1056
   5-fold covers : {30,22}*1320, {6,110}*1320
   6-fold covers : {36,22}*1584, {18,44}*1584a, {6,132}*1584a, {12,66}*1584a, {12,66}*1584b, {6,132}*1584b
   7-fold covers : {42,22}*1848, {6,154}*1848
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 : None.
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