Polytope of Type {5,2,14,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,14,2}*560
if this polytope has a name.
Group : SmallGroup(560,176)
Rank : 5
Schlafli Type : {5,2,14,2}
Number of vertices, edges, etc : 5, 5, 14, 14, 2
Order of s0s1s2s3s4 : 70
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,2,14,2,2} of size 1120
   {5,2,14,2,3} of size 1680
Vertex Figure Of :
   {2,5,2,14,2} of size 1120
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,2,7,2}*280
   7-fold quotients : {5,2,2,2}*80
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,2,28,2}*1120, {5,2,14,4}*1120, {10,2,14,2}*1120
   3-fold covers : {5,2,14,6}*1680, {15,2,14,2}*1680, {5,2,42,2}*1680
Permutation Representation (GAP) :
s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := ( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19);;
s3 := ( 6,10)( 7, 8)( 9,14)(11,12)(13,18)(15,16)(17,19);;
s4 := (20,21);;
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, 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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(21)!(2,3)(4,5);
s1 := Sym(21)!(1,2)(3,4);
s2 := Sym(21)!( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19);
s3 := Sym(21)!( 6,10)( 7, 8)( 9,14)(11,12)(13,18)(15,16)(17,19);
s4 := Sym(21)!(20,21);
poly := sub<Sym(21)|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, 
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 >; 
 

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