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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,2,9,4}*864
if this polytope has a name.
Group : SmallGroup(864,3999)
Rank : 6
Schlafli Type : {3,2,2,9,4}
Number of vertices, edges, etc : 3, 3, 2, 9, 18, 4
Order of s₀s₁s₂s₃s₄s₅ : 18
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,2,9,4,2} of size 1728
Vertex Figure Of :
   {2,3,2,2,9,4} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {3,2,2,3,4}*288
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,2,9,4}*1728, {3,2,2,18,4}*1728b, {3,2,2,18,4}*1728c, {6,2,2,9,4}*1728
Permutation Representation (GAP) :

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