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Polytope of Type {13,2,8,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {13,2,8,2}*832
if this polytope has a name.
Group : SmallGroup(832,1425)
Rank : 5
Schlafli Type : {13,2,8,2}
Number of vertices, edges, etc : 13, 13, 8, 8, 2
Order of s0s1s2s3s4 : 104
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {13,2,8,2,2} of size 1664
Vertex Figure Of :
   {2,13,2,8,2} of size 1664
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {13,2,4,2}*416
   4-fold quotients : {13,2,2,2}*208
Covers (Minimal Covers in Boldface) :
   2-fold covers : {13,2,8,4}*1664a, {13,2,16,2}*1664, {26,2,8,2}*1664
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12);;
s2 := (15,16)(17,18)(19,20);;
s3 := (14,15)(16,17)(18,19)(20,21);;
s4 := (22,23);;
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, 
s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*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(23)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13);
s1 := Sym(23)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12);
s2 := Sym(23)!(15,16)(17,18)(19,20);
s3 := Sym(23)!(14,15)(16,17)(18,19)(20,21);
s4 := Sym(23)!(22,23);
poly := sub<Sym(23)|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, s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*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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