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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,2,12,6}*1728b
if this polytope has a name.
Group : SmallGroup(1728,47319)
Rank : 6
Schlafli Type : {3,2,2,12,6}
Number of vertices, edges, etc : 3, 3, 2, 12, 36, 6
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 : {3,2,2,6,6}*864c
   3-fold quotients : {3,2,2,12,2}*576
   4-fold quotients : {3,2,2,3,6}*432
   6-fold quotients : {3,2,2,6,2}*288
   9-fold quotients : {3,2,2,4,2}*192
   12-fold quotients : {3,2,2,3,2}*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 := (4,5);;
s3 := ( 6,42)( 7,44)( 8,43)( 9,48)(10,50)(11,49)(12,45)(13,47)(14,46)(15,51)
(16,53)(17,52)(18,57)(19,59)(20,58)(21,54)(22,56)(23,55)(24,69)(25,71)(26,70)
(27,75)(28,77)(29,76)(30,72)(31,74)(32,73)(33,60)(34,62)(35,61)(36,66)(37,68)
(38,67)(39,63)(40,65)(41,64);;
s4 := ( 6,64)( 7,63)( 8,65)( 9,61)(10,60)(11,62)(12,67)(13,66)(14,68)(15,73)
(16,72)(17,74)(18,70)(19,69)(20,71)(21,76)(22,75)(23,77)(24,46)(25,45)(26,47)
(27,43)(28,42)(29,44)(30,49)(31,48)(32,50)(33,55)(34,54)(35,56)(36,52)(37,51)
(38,53)(39,58)(40,57)(41,59);;
s5 := ( 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)(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, 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, s5*s3*s4*s5*s4*s5*s3*s4*s5*s4, 
s3*s4*s5*s4*s3*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*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope