Polytope of Type {9,2,4,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,2,4,6}*864c
if this polytope has a name.
Group : SmallGroup(864,3998)
Rank : 5
Schlafli Type : {9,2,4,6}
Number of vertices, edges, etc : 9, 9, 4, 12, 6
Order of s₀s₁s₂s₃s₄ : 18
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {9,2,4,6,2} of size 1728
Vertex Figure Of :
   {2,9,2,4,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {9,2,4,3}*432
   3-fold quotients : {3,2,4,6}*288c
   6-fold quotients : {3,2,4,3}*144
Covers (Minimal Covers in Boldface) :
   2-fold covers : {9,2,4,12}*1728b, {9,2,4,12}*1728c, {9,2,4,6}*1728, {18,2,4,6}*1728c
Permutation Representation (GAP) :

s0 := (2,3)(4,5)(6,7)(8,9);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (12,14)(13,15);;
s3 := (10,12)(11,14);;
s4 := (10,11)(12,13)(14,15);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, 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, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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(15)!(2,3)(4,5)(6,7)(8,9);
s1 := Sym(15)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(15)!(12,14)(13,15);
s3 := Sym(15)!(10,12)(11,14);
s4 := Sym(15)!(10,11)(12,13)(14,15);
poly := sub<Sym(15)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, 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, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

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