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Polytope of Type {66}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {66}*132
Also Known As : 66-gon, {66}. if this polytope has another name.
Group : SmallGroup(132,9)
Rank : 2
Schlafli Type : {66}
Number of vertices, edges, etc : 66, 66
Order of s0s1 : 66
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {66,2} of size 264
   {66,4} of size 528
   {66,4} of size 528
   {66,4} of size 528
   {66,6} of size 792
   {66,6} of size 792
   {66,6} of size 792
   {66,8} of size 1056
   {66,6} of size 1056
   {66,4} of size 1056
   {66,6} of size 1188
   {66,10} of size 1320
   {66,12} of size 1584
   {66,12} of size 1584
   {66,12} of size 1584
   {66,4} of size 1584
   {66,12} of size 1584
   {66,14} of size 1848
Vertex Figure Of :
   {2,66} of size 264
   {4,66} of size 528
   {4,66} of size 528
   {4,66} of size 528
   {6,66} of size 792
   {6,66} of size 792
   {6,66} of size 792
   {8,66} of size 1056
   {6,66} of size 1056
   {4,66} of size 1056
   {6,66} of size 1188
   {10,66} of size 1320
   {12,66} of size 1584
   {12,66} of size 1584
   {12,66} of size 1584
   {4,66} of size 1584
   {12,66} of size 1584
   {14,66} of size 1848
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {33}*66
   3-fold quotients : {22}*44
   6-fold quotients : {11}*22
   11-fold quotients : {6}*12
   22-fold quotients : {3}*6
   33-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   2-fold covers : {132}*264
   3-fold covers : {198}*396
   4-fold covers : {264}*528
   5-fold covers : {330}*660
   6-fold covers : {396}*792
   7-fold covers : {462}*924
   8-fold covers : {528}*1056
   9-fold covers : {594}*1188
   10-fold covers : {660}*1320
   11-fold covers : {726}*1452
   12-fold covers : {792}*1584
   13-fold covers : {858}*1716
   14-fold covers : {924}*1848
   15-fold covers : {990}*1980
Permutation Representation (GAP) :
s0 := ( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)(12,23)(13,33)(14,32)(15,31)(16,30)
(17,29)(18,28)(19,27)(20,26)(21,25)(22,24)(35,44)(36,43)(37,42)(38,41)(39,40)
(45,56)(46,66)(47,65)(48,64)(49,63)(50,62)(51,61)(52,60)(53,59)(54,58)
(55,57);;
s1 := ( 1,46)( 2,45)( 3,55)( 4,54)( 5,53)( 6,52)( 7,51)( 8,50)( 9,49)(10,48)
(11,47)(12,35)(13,34)(14,44)(15,43)(16,42)(17,41)(18,40)(19,39)(20,38)(21,37)
(22,36)(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]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1");;
s0 := F.1;;  s1 := F.2;;  
rels := [ s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(66)!( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)(12,23)(13,33)(14,32)(15,31)
(16,30)(17,29)(18,28)(19,27)(20,26)(21,25)(22,24)(35,44)(36,43)(37,42)(38,41)
(39,40)(45,56)(46,66)(47,65)(48,64)(49,63)(50,62)(51,61)(52,60)(53,59)(54,58)
(55,57);
s1 := Sym(66)!( 1,46)( 2,45)( 3,55)( 4,54)( 5,53)( 6,52)( 7,51)( 8,50)( 9,49)
(10,48)(11,47)(12,35)(13,34)(14,44)(15,43)(16,42)(17,41)(18,40)(19,39)(20,38)
(21,37)(22,36)(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>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
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