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

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

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

Permutation Representation (Magma) :

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

to this polytope