Polytope of Type {3,2,2,4,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,2,4,6}*1728
if this polytope has a name.
Group : SmallGroup(1728,47887)
Rank : 6
Schlafli Type : {3,2,2,4,6}
Number of vertices, edges, etc : 3, 3, 2, 12, 36, 18
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 : {3,2,2,4,6}*864
   9-fold quotients : {3,2,2,4,2}*192
   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 := (4,5);;
s3 := ( 9,12)(10,13)(11,14)(18,21)(19,22)(20,23)(27,30)(28,31)(29,32)(36,39)
(37,40)(38,41)(42,51)(43,52)(44,53)(45,57)(46,58)(47,59)(48,54)(49,55)(50,56)
(60,69)(61,70)(62,71)(63,75)(64,76)(65,77)(66,72)(67,73)(68,74);;
s4 := ( 6,42)( 7,45)( 8,48)( 9,43)(10,46)(11,49)(12,44)(13,47)(14,50)(15,51)
(16,54)(17,57)(18,52)(19,55)(20,58)(21,53)(22,56)(23,59)(24,60)(25,63)(26,66)
(27,61)(28,64)(29,67)(30,62)(31,65)(32,68)(33,69)(34,72)(35,75)(36,70)(37,73)
(38,76)(39,71)(40,74)(41,77);;
s5 := ( 6,34)( 7,33)( 8,35)( 9,40)(10,39)(11,41)(12,37)(13,36)(14,38)(15,25)
(16,24)(17,26)(18,31)(19,30)(20,32)(21,28)(22,27)(23,29)(42,70)(43,69)(44,71)
(45,76)(46,75)(47,77)(48,73)(49,72)(50,74)(51,61)(52,60)(53,62)(54,67)(55,66)
(56,68)(57,64)(58,63)(59,65);;
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, 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, 
s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4, 
s5*s3*s4*s5*s3*s4*s5*s3*s4*s5*s3*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(77)!(2,3);
s1 := Sym(77)!(1,2);
s2 := Sym(77)!(4,5);
s3 := Sym(77)!( 9,12)(10,13)(11,14)(18,21)(19,22)(20,23)(27,30)(28,31)(29,32)
(36,39)(37,40)(38,41)(42,51)(43,52)(44,53)(45,57)(46,58)(47,59)(48,54)(49,55)
(50,56)(60,69)(61,70)(62,71)(63,75)(64,76)(65,77)(66,72)(67,73)(68,74);
s4 := Sym(77)!( 6,42)( 7,45)( 8,48)( 9,43)(10,46)(11,49)(12,44)(13,47)(14,50)
(15,51)(16,54)(17,57)(18,52)(19,55)(20,58)(21,53)(22,56)(23,59)(24,60)(25,63)
(26,66)(27,61)(28,64)(29,67)(30,62)(31,65)(32,68)(33,69)(34,72)(35,75)(36,70)
(37,73)(38,76)(39,71)(40,74)(41,77);
s5 := Sym(77)!( 6,34)( 7,33)( 8,35)( 9,40)(10,39)(11,41)(12,37)(13,36)(14,38)
(15,25)(16,24)(17,26)(18,31)(19,30)(20,32)(21,28)(22,27)(23,29)(42,70)(43,69)
(44,71)(45,76)(46,75)(47,77)(48,73)(49,72)(50,74)(51,61)(52,60)(53,62)(54,67)
(55,66)(56,68)(57,64)(58,63)(59,65);
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, 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, s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4, 
s5*s3*s4*s5*s3*s4*s5*s3*s4*s5*s3*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;

to this polytope