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}*1728a
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}*864a
   3-fold quotients : {3,2,2,12,2}*576, {3,2,2,4,6}*576a
   6-fold quotients : {3,2,2,2,6}*288, {3,2,2,6,2}*288
   9-fold quotients : {3,2,2,4,2}*192
   12-fold quotients : {3,2,2,2,3}*144, {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)( 7,43)( 8,44)( 9,48)(10,49)(11,50)(12,45)(13,46)(14,47)(15,51)
(16,52)(17,53)(18,57)(19,58)(20,59)(21,54)(22,55)(23,56)(24,69)(25,70)(26,71)
(27,75)(28,76)(29,77)(30,72)(31,73)(32,74)(33,60)(34,61)(35,62)(36,66)(37,67)
(38,68)(39,63)(40,64)(41,65);;
s4 := ( 6,63)( 7,65)( 8,64)( 9,60)(10,62)(11,61)(12,66)(13,68)(14,67)(15,72)
(16,74)(17,73)(18,69)(19,71)(20,70)(21,75)(22,77)(23,76)(24,45)(25,47)(26,46)
(27,42)(28,44)(29,43)(30,48)(31,50)(32,49)(33,54)(34,56)(35,55)(36,51)(37,53)
(38,52)(39,57)(40,59)(41,58);;
s5 := ( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)(33,34)
(36,37)(39,40)(42,43)(45,46)(48,49)(51,52)(54,55)(57,58)(60,61)(63,64)(66,67)
(69,70)(72,73)(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*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*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, 
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)( 7,43)( 8,44)( 9,48)(10,49)(11,50)(12,45)(13,46)(14,47)
(15,51)(16,52)(17,53)(18,57)(19,58)(20,59)(21,54)(22,55)(23,56)(24,69)(25,70)
(26,71)(27,75)(28,76)(29,77)(30,72)(31,73)(32,74)(33,60)(34,61)(35,62)(36,66)
(37,67)(38,68)(39,63)(40,64)(41,65);
s4 := Sym(77)!( 6,63)( 7,65)( 8,64)( 9,60)(10,62)(11,61)(12,66)(13,68)(14,67)
(15,72)(16,74)(17,73)(18,69)(19,71)(20,70)(21,75)(22,77)(23,76)(24,45)(25,47)
(26,46)(27,42)(28,44)(29,43)(30,48)(31,50)(32,49)(33,54)(34,56)(35,55)(36,51)
(37,53)(38,52)(39,57)(40,59)(41,58);
s5 := Sym(77)!( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)
(33,34)(36,37)(39,40)(42,43)(45,46)(48,49)(51,52)(54,55)(57,58)(60,61)(63,64)
(66,67)(69,70)(72,73)(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*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*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, 
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