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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,4,2,2,4}*1152
if this polytope has a name.
Group : SmallGroup(1152,155402)
Rank : 6
Schlafli Type : {9,4,2,2,4}
Number of vertices, edges, etc : 9, 18, 4, 2, 4, 4
Order of s₀s₁s₂s₃s₄s₅ : 36
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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 : {9,4,2,2,2}*576
   3-fold quotients : {3,4,2,2,4}*384
   6-fold quotients : {3,4,2,2,2}*192
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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