Polytope of Type {2,3,2,18,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,2,18,4}*1728a
if this polytope has a name.
Group : SmallGroup(1728,30790)
Rank : 6
Schlafli Type : {2,3,2,18,4}
Number of vertices, edges, etc : 2, 3, 3, 18, 36, 4
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 : {2,3,2,18,2}*864
   3-fold quotients : {2,3,2,6,4}*576a
   4-fold quotients : {2,3,2,9,2}*432
   6-fold quotients : {2,3,2,6,2}*288
   9-fold quotients : {2,3,2,2,4}*192
   12-fold quotients : {2,3,2,3,2}*144
   18-fold quotients : {2,3,2,2,2}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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