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Polytope of Type {2,2,2,10,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,10,12}*1920
if this polytope has a name.
Group : SmallGroup(1920,236182)
Rank : 6
Schlafli Type : {2,2,2,10,12}
Number of vertices, edges, etc : 2, 2, 2, 10, 60, 12
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 : {2,2,2,10,4}*640
   5-fold quotients : {2,2,2,2,12}*384
   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 : {2,2,2,2,4}*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)(38,41)(39,40)(43,46)(44,45)(48,51)(49,50)(53,56)(54,55)(58,61)
(59,60)(63,66)(64,65);;
s4 := ( 7, 8)( 9,11)(12,18)(13,17)(14,21)(15,20)(16,19)(22,23)(24,26)(27,33)
(28,32)(29,36)(30,35)(31,34)(37,53)(38,52)(39,56)(40,55)(41,54)(42,63)(43,62)
(44,66)(45,65)(46,64)(47,58)(48,57)(49,61)(50,60)(51,59);;
s5 := ( 7,42)( 8,43)( 9,44)(10,45)(11,46)(12,37)(13,38)(14,39)(15,40)(16,41)
(17,47)(18,48)(19,49)(20,50)(21,51)(22,57)(23,58)(24,59)(25,60)(26,61)(27,52)
(28,53)(29,54)(30,55)(31,56)(32,62)(33,63)(34,64)(35,65)(36,66);;
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, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
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)(38,41)(39,40)(43,46)(44,45)(48,51)(49,50)(53,56)(54,55)
(58,61)(59,60)(63,66)(64,65);
s4 := Sym(66)!( 7, 8)( 9,11)(12,18)(13,17)(14,21)(15,20)(16,19)(22,23)(24,26)
(27,33)(28,32)(29,36)(30,35)(31,34)(37,53)(38,52)(39,56)(40,55)(41,54)(42,63)
(43,62)(44,66)(45,65)(46,64)(47,58)(48,57)(49,61)(50,60)(51,59);
s5 := Sym(66)!( 7,42)( 8,43)( 9,44)(10,45)(11,46)(12,37)(13,38)(14,39)(15,40)
(16,41)(17,47)(18,48)(19,49)(20,50)(21,51)(22,57)(23,58)(24,59)(25,60)(26,61)
(27,52)(28,53)(29,54)(30,55)(31,56)(32,62)(33,63)(34,64)(35,65)(36,66);
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, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >; 
 

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