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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,2,4,6,3}*1728
if this polytope has a name.
Group : SmallGroup(1728,47409)
Rank : 7
Schlafli Type : {3,2,2,4,6,3}
Number of vertices, edges, etc : 3, 3, 2, 4, 12, 9, 3
Order of s₀s₁s₂s₃s₄s₅s₆ : 12
Order of s₀s₁s₂s₃s₄s₅s₆s₅s₄s₃s₂s₁ : 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 : {3,2,2,2,6,3}*864
   3-fold quotients : {3,2,2,4,2,3}*576
   6-fold quotients : {3,2,2,2,2,3}*288
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := (4,5);;
s3 := ( 6,24)( 7,25)( 8,26)( 9,27)(10,28)(11,29)(12,30)(13,31)(14,32)(15,33)
(16,34)(17,35)(18,36)(19,37)(20,38)(21,39)(22,40)(23,41)(42,60)(43,61)(44,62)
(45,63)(46,64)(47,65)(48,66)(49,67)(50,68)(51,69)(52,70)(53,71)(54,72)(55,73)
(56,74)(57,75)(58,76)(59,77);;
s4 := ( 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);;
s5 := ( 6,43)( 7,42)( 8,44)( 9,49)(10,48)(11,50)(12,46)(13,45)(14,47)(15,52)
(16,51)(17,53)(18,58)(19,57)(20,59)(21,55)(22,54)(23,56)(24,61)(25,60)(26,62)
(27,67)(28,66)(29,68)(30,64)(31,63)(32,65)(33,70)(34,69)(35,71)(36,76)(37,75)
(38,77)(39,73)(40,72)(41,74);;
s6 := ( 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,s6]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5","s6");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  s6 := F.7;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s6*s6, 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*s6*s0*s6, s1*s6*s1*s6, s2*s6*s2*s6, 
s3*s6*s3*s6, s4*s6*s4*s6, s0*s1*s0*s1*s0*s1, 
s5*s6*s5*s6*s5*s6, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s5*s4, s6*s4*s5*s4*s5*s6*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)!( 6,24)( 7,25)( 8,26)( 9,27)(10,28)(11,29)(12,30)(13,31)(14,32)
(15,33)(16,34)(17,35)(18,36)(19,37)(20,38)(21,39)(22,40)(23,41)(42,60)(43,61)
(44,62)(45,63)(46,64)(47,65)(48,66)(49,67)(50,68)(51,69)(52,70)(53,71)(54,72)
(55,73)(56,74)(57,75)(58,76)(59,77);
s4 := 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);
s5 := Sym(77)!( 6,43)( 7,42)( 8,44)( 9,49)(10,48)(11,50)(12,46)(13,45)(14,47)
(15,52)(16,51)(17,53)(18,58)(19,57)(20,59)(21,55)(22,54)(23,56)(24,61)(25,60)
(26,62)(27,67)(28,66)(29,68)(30,64)(31,63)(32,65)(33,70)(34,69)(35,71)(36,76)
(37,75)(38,77)(39,73)(40,72)(41,74);
s6 := 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,s6>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5,s6> := Group< s0,s1,s2,s3,s4,s5,s6 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s6*s6, 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*s6*s0*s6, 
s1*s6*s1*s6, s2*s6*s2*s6, s3*s6*s3*s6, 
s4*s6*s4*s6, s0*s1*s0*s1*s0*s1, s5*s6*s5*s6*s5*s6, 
s3*s4*s3*s4*s3*s4*s3*s4, s3*s4*s5*s4*s3*s4*s5*s4, 
s6*s4*s5*s4*s5*s6*s4*s5*s4*s5 >;

to this polytope