Polytope of Type {4,3,2,13}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,3,2,13}*624
if this polytope has a name.
Group : SmallGroup(624,242)
Rank : 5
Schlafli Type : {4,3,2,13}
Number of vertices, edges, etc : 4, 6, 3, 13, 13
Order of s₀s₁s₂s₃s₄ : 39
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,3,2,13,2} of size 1248
Vertex Figure Of :
   {2,4,3,2,13} of size 1248
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,3,2,13}*1248, {4,3,2,26}*1248, {4,6,2,13}*1248b, {4,6,2,13}*1248c
   3-fold covers : {4,9,2,13}*1872, {4,3,2,39}*1872
Permutation Representation (GAP) :

s0 := (1,2)(3,4);;
s1 := (2,3);;
s2 := (3,4);;
s3 := ( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17);;
s4 := ( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1, s3*s4*s3*s4*s3*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(17)!(1,2)(3,4);
s1 := Sym(17)!(2,3);
s2 := Sym(17)!(3,4);
s3 := Sym(17)!( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17);
s4 := Sym(17)!( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);
poly := sub<Sym(17)|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, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s3*s4*s3*s4*s3*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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