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

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