Polytope of Type {5,2,7,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,7,2}*280
if this polytope has a name.
Group : SmallGroup(280,36)
Rank : 5
Schlafli Type : {5,2,7,2}
Number of vertices, edges, etc : 5, 5, 7, 7, 2
Order of s₀s₁s₂s₃s₄ : 70
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,2,7,2,2} of size 560
   {5,2,7,2,3} of size 840
   {5,2,7,2,4} of size 1120
   {5,2,7,2,5} of size 1400
   {5,2,7,2,6} of size 1680
   {5,2,7,2,7} of size 1960
Vertex Figure Of :
   {2,5,2,7,2} of size 560
   {3,5,2,7,2} of size 1680
   {5,5,2,7,2} of size 1680
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,2,14,2}*560, {10,2,7,2}*560
   3-fold covers : {15,2,7,2}*840, {5,2,21,2}*840
   4-fold covers : {20,2,7,2}*1120, {5,2,28,2}*1120, {5,2,14,4}*1120, {10,2,14,2}*1120
   5-fold covers : {25,2,7,2}*1400, {5,2,35,2}*1400
   6-fold covers : {5,2,14,6}*1680, {15,2,14,2}*1680, {30,2,7,2}*1680, {5,2,42,2}*1680, {10,2,21,2}*1680
   7-fold covers : {5,2,49,2}*1960, {5,2,7,14}*1960, {35,2,7,2}*1960
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope