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Polytope of Type {6,22,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,22,2}*528
if this polytope has a name.
Group : SmallGroup(528,164)
Rank : 4
Schlafli Type : {6,22,2}
Number of vertices, edges, etc : 6, 66, 22, 2
Order of s0s1s2s3 : 66
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,22,2,2} of size 1056
   {6,22,2,3} of size 1584
Vertex Figure Of :
   {2,6,22,2} of size 1056
   {3,6,22,2} of size 1584
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,22,2}*176
   6-fold quotients : {2,11,2}*88
   11-fold quotients : {6,2,2}*48
   22-fold quotients : {3,2,2}*24
   33-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,22,2}*1056, {6,44,2}*1056a, {6,22,4}*1056
   3-fold covers : {18,22,2}*1584, {6,22,6}*1584, {6,66,2}*1584a, {6,66,2}*1584b
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);;
s3 := (67,68);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
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(68)!(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(68)!( 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(68)!( 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);
s3 := Sym(68)!(67,68);
poly := sub<Sym(68)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, 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 >; 
 

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