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

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

Permutation Representation (Magma) :

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

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