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Polytope of Type {2,6,12,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,12,2,3}*1728a
if this polytope has a name.
Group : SmallGroup(1728,47319)
Rank : 6
Schlafli Type : {2,6,12,2,3}
Number of vertices, edges, etc : 2, 6, 36, 12, 3, 3
Order of s0s1s2s3s4s5 : 12
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 : {2,6,6,2,3}*864a
   3-fold quotients : {2,2,12,2,3}*576, {2,6,4,2,3}*576a
   6-fold quotients : {2,2,6,2,3}*288, {2,6,2,2,3}*288
   9-fold quotients : {2,2,4,2,3}*192
   12-fold quotients : {2,2,3,2,3}*144, {2,3,2,2,3}*144
   18-fold quotients : {2,2,2,2,3}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)
(34,35)(37,38)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)(58,59)(61,62)(64,65)
(67,68)(70,71)(73,74);;
s2 := ( 3,40)( 4,39)( 5,41)( 6,46)( 7,45)( 8,47)( 9,43)(10,42)(11,44)(12,49)
(13,48)(14,50)(15,55)(16,54)(17,56)(18,52)(19,51)(20,53)(21,67)(22,66)(23,68)
(24,73)(25,72)(26,74)(27,70)(28,69)(29,71)(30,58)(31,57)(32,59)(33,64)(34,63)
(35,65)(36,61)(37,60)(38,62);;
s3 := ( 3,60)( 4,61)( 5,62)( 6,57)( 7,58)( 8,59)( 9,63)(10,64)(11,65)(12,69)
(13,70)(14,71)(15,66)(16,67)(17,68)(18,72)(19,73)(20,74)(21,42)(22,43)(23,44)
(24,39)(25,40)(26,41)(27,45)(28,46)(29,47)(30,51)(31,52)(32,53)(33,48)(34,49)
(35,50)(36,54)(37,55)(38,56);;
s4 := (76,77);;
s5 := (75,76);;
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, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5*s4*s5, s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(77)!(1,2);
s1 := Sym(77)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)
(31,32)(34,35)(37,38)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)(58,59)(61,62)
(64,65)(67,68)(70,71)(73,74);
s2 := Sym(77)!( 3,40)( 4,39)( 5,41)( 6,46)( 7,45)( 8,47)( 9,43)(10,42)(11,44)
(12,49)(13,48)(14,50)(15,55)(16,54)(17,56)(18,52)(19,51)(20,53)(21,67)(22,66)
(23,68)(24,73)(25,72)(26,74)(27,70)(28,69)(29,71)(30,58)(31,57)(32,59)(33,64)
(34,63)(35,65)(36,61)(37,60)(38,62);
s3 := Sym(77)!( 3,60)( 4,61)( 5,62)( 6,57)( 7,58)( 8,59)( 9,63)(10,64)(11,65)
(12,69)(13,70)(14,71)(15,66)(16,67)(17,68)(18,72)(19,73)(20,74)(21,42)(22,43)
(23,44)(24,39)(25,40)(26,41)(27,45)(28,46)(29,47)(30,51)(31,52)(32,53)(33,48)
(34,49)(35,50)(36,54)(37,55)(38,56);
s4 := Sym(77)!(76,77);
s5 := Sym(77)!(75,76);
poly := sub<Sym(77)|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, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5*s4*s5, s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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