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Polytope of Type {2,2,2,20,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,20,6}*1920a
if this polytope has a name.
Group : SmallGroup(1920,236184)
Rank : 6
Schlafli Type : {2,2,2,20,6}
Number of vertices, edges, etc : 2, 2, 2, 20, 60, 6
Order of s0s1s2s3s4s5 : 60
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,2,10,6}*960
   3-fold quotients : {2,2,2,20,2}*640
   5-fold quotients : {2,2,2,4,6}*384a
   6-fold quotients : {2,2,2,10,2}*320
   10-fold quotients : {2,2,2,2,6}*192
   12-fold quotients : {2,2,2,5,2}*160
   15-fold quotients : {2,2,2,4,2}*128
   20-fold quotients : {2,2,2,2,3}*96
   30-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := ( 8,11)( 9,10)(13,16)(14,15)(18,21)(19,20)(23,26)(24,25)(28,31)(29,30)
(33,36)(34,35)(37,52)(38,56)(39,55)(40,54)(41,53)(42,57)(43,61)(44,60)(45,59)
(46,58)(47,62)(48,66)(49,65)(50,64)(51,63);;
s4 := ( 7,38)( 8,37)( 9,41)(10,40)(11,39)(12,48)(13,47)(14,51)(15,50)(16,49)
(17,43)(18,42)(19,46)(20,45)(21,44)(22,53)(23,52)(24,56)(25,55)(26,54)(27,63)
(28,62)(29,66)(30,65)(31,64)(32,58)(33,57)(34,61)(35,60)(36,59);;
s5 := ( 7,12)( 8,13)( 9,14)(10,15)(11,16)(22,27)(23,28)(24,29)(25,30)(26,31)
(37,42)(38,43)(39,44)(40,45)(41,46)(52,57)(53,58)(54,59)(55,60)(56,61);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s3*s4*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(66)!(1,2);
s1 := Sym(66)!(3,4);
s2 := Sym(66)!(5,6);
s3 := Sym(66)!( 8,11)( 9,10)(13,16)(14,15)(18,21)(19,20)(23,26)(24,25)(28,31)
(29,30)(33,36)(34,35)(37,52)(38,56)(39,55)(40,54)(41,53)(42,57)(43,61)(44,60)
(45,59)(46,58)(47,62)(48,66)(49,65)(50,64)(51,63);
s4 := Sym(66)!( 7,38)( 8,37)( 9,41)(10,40)(11,39)(12,48)(13,47)(14,51)(15,50)
(16,49)(17,43)(18,42)(19,46)(20,45)(21,44)(22,53)(23,52)(24,56)(25,55)(26,54)
(27,63)(28,62)(29,66)(30,65)(31,64)(32,58)(33,57)(34,61)(35,60)(36,59);
s5 := Sym(66)!( 7,12)( 8,13)( 9,14)(10,15)(11,16)(22,27)(23,28)(24,29)(25,30)
(26,31)(37,42)(38,43)(39,44)(40,45)(41,46)(52,57)(53,58)(54,59)(55,60)(56,61);
poly := sub<Sym(66)|s0,s1,s2,s3,s4,s5>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s3*s4*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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