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

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

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

Permutation Representation (Magma) :

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

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