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}*1728c
if this polytope has a name.
Group : SmallGroup(1728,47409)
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}*864b
   3-fold quotients : {3,2,2,4,6}*576a
   4-fold quotients : {3,2,2,6,3}*432
   6-fold quotients : {3,2,2,2,6}*288
   9-fold quotients : {3,2,2,4,2}*192
   12-fold quotients : {3,2,2,2,3}*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 := ( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(24,33)(25,35)(26,34)(27,36)
(28,38)(29,37)(30,39)(31,41)(32,40)(43,44)(46,47)(49,50)(52,53)(55,56)(58,59)
(60,69)(61,71)(62,70)(63,72)(64,74)(65,73)(66,75)(67,77)(68,76);;
s4 := ( 6,61)( 7,60)( 8,62)( 9,67)(10,66)(11,68)(12,64)(13,63)(14,65)(15,70)
(16,69)(17,71)(18,76)(19,75)(20,77)(21,73)(22,72)(23,74)(24,43)(25,42)(26,44)
(27,49)(28,48)(29,50)(30,46)(31,45)(32,47)(33,52)(34,51)(35,53)(36,58)(37,57)
(38,59)(39,55)(40,54)(41,56);;
s5 := ( 6,45)( 7,47)( 8,46)( 9,42)(10,44)(11,43)(12,48)(13,50)(14,49)(15,54)
(16,56)(17,55)(18,51)(19,53)(20,52)(21,57)(22,59)(23,58)(24,63)(25,65)(26,64)
(27,60)(28,62)(29,61)(30,66)(31,68)(32,67)(33,72)(34,74)(35,73)(36,69)(37,71)
(38,70)(39,75)(40,77)(41,76);;
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, s5*s3*s4*s3*s4*s5*s3*s4*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)!( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(24,33)(25,35)(26,34)
(27,36)(28,38)(29,37)(30,39)(31,41)(32,40)(43,44)(46,47)(49,50)(52,53)(55,56)
(58,59)(60,69)(61,71)(62,70)(63,72)(64,74)(65,73)(66,75)(67,77)(68,76);
s4 := Sym(77)!( 6,61)( 7,60)( 8,62)( 9,67)(10,66)(11,68)(12,64)(13,63)(14,65)
(15,70)(16,69)(17,71)(18,76)(19,75)(20,77)(21,73)(22,72)(23,74)(24,43)(25,42)
(26,44)(27,49)(28,48)(29,50)(30,46)(31,45)(32,47)(33,52)(34,51)(35,53)(36,58)
(37,57)(38,59)(39,55)(40,54)(41,56);
s5 := Sym(77)!( 6,45)( 7,47)( 8,46)( 9,42)(10,44)(11,43)(12,48)(13,50)(14,49)
(15,54)(16,56)(17,55)(18,51)(19,53)(20,52)(21,57)(22,59)(23,58)(24,63)(25,65)
(26,64)(27,60)(28,62)(29,61)(30,66)(31,68)(32,67)(33,72)(34,74)(35,73)(36,69)
(37,71)(38,70)(39,75)(40,77)(41,76);
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, s5*s3*s4*s3*s4*s5*s3*s4*s3*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;

to this polytope