Polytope of Type {3,2,2,4,9}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,2,4,9}*1728
if this polytope has a name.
Group : SmallGroup(1728,46115)
Rank : 6
Schlafli Type : {3,2,2,4,9}
Number of vertices, edges, etc : 3, 3, 2, 8, 36, 18
Order of s₀s₁s₂s₃s₄s₅ : 18
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 : {3,2,2,4,9}*864
   3-fold quotients : {3,2,2,4,3}*576
   4-fold quotients : {3,2,2,2,9}*432
   6-fold quotients : {3,2,2,4,3}*288
   12-fold quotients : {3,2,2,2,3}*144
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

to this polytope