Polytope of Type {9,2,22}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,2,22}*792
if this polytope has a name.
Group : SmallGroup(792,40)
Rank : 4
Schlafli Type : {9,2,22}
Number of vertices, edges, etc : 9, 9, 22, 22
Order of s₀s₁s₂s₃ : 198
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {9,2,22,2} of size 1584
Vertex Figure Of :
   {2,9,2,22} of size 1584
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {9,2,11}*396
   3-fold quotients : {3,2,22}*264
   6-fold quotients : {3,2,11}*132
   11-fold quotients : {9,2,2}*72
   33-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {9,2,44}*1584, {18,2,22}*1584
Permutation Representation (GAP) :

s0 := (2,3)(4,5)(6,7)(8,9);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31);;
s3 := (10,14)(11,12)(13,18)(15,16)(17,22)(19,20)(21,26)(23,24)(25,30)(27,28)
(29,31);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(31)!(2,3)(4,5)(6,7)(8,9);
s1 := Sym(31)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(31)!(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)
(30,31);
s3 := Sym(31)!(10,14)(11,12)(13,18)(15,16)(17,22)(19,20)(21,26)(23,24)(25,30)
(27,28)(29,31);
poly := sub<Sym(31)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

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

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