Polytope of Type {7,2,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,2,10}*280
if this polytope has a name.
Group : SmallGroup(280,36)
Rank : 4
Schlafli Type : {7,2,10}
Number of vertices, edges, etc : 7, 7, 10, 10
Order of s₀s₁s₂s₃ : 70
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {7,2,10,2} of size 560
   {7,2,10,4} of size 1120
   {7,2,10,5} of size 1400
   {7,2,10,3} of size 1680
   {7,2,10,3} of size 1680
   {7,2,10,5} of size 1680
   {7,2,10,5} of size 1680
   {7,2,10,6} of size 1680
Vertex Figure Of :
   {2,7,2,10} of size 560
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {7,2,5}*140
   5-fold quotients : {7,2,2}*56
Covers (Minimal Covers in Boldface) :
   2-fold covers : {7,2,20}*560, {14,2,10}*560
   3-fold covers : {7,2,30}*840, {21,2,10}*840
   4-fold covers : {7,2,40}*1120, {14,2,20}*1120, {28,2,10}*1120, {14,4,10}*1120
   5-fold covers : {7,2,50}*1400, {35,2,10}*1400
   6-fold covers : {7,2,60}*1680, {21,2,20}*1680, {14,6,10}*1680, {14,2,30}*1680, {42,2,10}*1680
   7-fold covers : {49,2,10}*1960, {7,14,10}*1960, {7,2,70}*1960
Permutation Representation (GAP) :

s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6);;
s2 := (10,11)(12,13)(14,15)(16,17);;
s3 := ( 8,12)( 9,10)(11,16)(13,14)(15,17);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*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 >;

to this polytope