Polytope of Type {3,2,36,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,36,2,2}*1728
if this polytope has a name.
Group : SmallGroup(1728,30764)
Rank : 6
Schlafli Type : {3,2,36,2,2}
Number of vertices, edges, etc : 3, 3, 36, 36, 2, 2
Order of s₀s₁s₂s₃s₄s₅ : 36
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 : {3,2,18,2,2}*864
   3-fold quotients : {3,2,12,2,2}*576
   4-fold quotients : {3,2,9,2,2}*432
   6-fold quotients : {3,2,6,2,2}*288
   9-fold quotients : {3,2,4,2,2}*192
   12-fold quotients : {3,2,3,2,2}*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 := ( 5, 6)( 7, 8)(10,13)(11,12)(14,15)(16,17)(18,21)(19,20)(22,23)(24,25)
(26,29)(27,28)(30,31)(32,33)(34,37)(35,36)(38,39);;
s3 := ( 4,10)( 5, 7)( 6,16)( 8,18)( 9,12)(11,14)(13,24)(15,26)(17,20)(19,22)
(21,32)(23,34)(25,28)(27,30)(29,38)(31,35)(33,36)(37,39);;
s4 := (40,41);;
s5 := (42,43);;
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, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(43)!(2,3);
s1 := Sym(43)!(1,2);
s2 := Sym(43)!( 5, 6)( 7, 8)(10,13)(11,12)(14,15)(16,17)(18,21)(19,20)(22,23)
(24,25)(26,29)(27,28)(30,31)(32,33)(34,37)(35,36)(38,39);
s3 := Sym(43)!( 4,10)( 5, 7)( 6,16)( 8,18)( 9,12)(11,14)(13,24)(15,26)(17,20)
(19,22)(21,32)(23,34)(25,28)(27,30)(29,38)(31,35)(33,36)(37,39);
s4 := Sym(43)!(40,41);
s5 := Sym(43)!(42,43);
poly := sub<Sym(43)|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, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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