Polytope of Type {7,2,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,2,5}*140
if this polytope has a name.
Group : SmallGroup(140,7)
Rank : 4
Schlafli Type : {7,2,5}
Number of vertices, edges, etc : 7, 7, 5, 5
Order of s₀s₁s₂s₃ : 35
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {7,2,5,2} of size 280
   {7,2,5,3} of size 840
   {7,2,5,5} of size 840
   {7,2,5,10} of size 1400
   {7,2,5,4} of size 1680
   {7,2,5,6} of size 1680
   {7,2,5,3} of size 1680
   {7,2,5,5} of size 1680
   {7,2,5,6} of size 1680
   {7,2,5,6} of size 1680
   {7,2,5,10} of size 1680
   {7,2,5,10} of size 1680
Vertex Figure Of :
   {2,7,2,5} of size 280
   {14,7,2,5} of size 1960
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {7,2,10}*280, {14,2,5}*280
   3-fold covers : {7,2,15}*420, {21,2,5}*420
   4-fold covers : {7,2,20}*560, {28,2,5}*560, {14,2,10}*560
   5-fold covers : {7,2,25}*700, {35,2,5}*700
   6-fold covers : {7,2,30}*840, {14,2,15}*840, {21,2,10}*840, {42,2,5}*840
   7-fold covers : {49,2,5}*980, {7,2,35}*980
   8-fold covers : {7,2,40}*1120, {56,2,5}*1120, {14,2,20}*1120, {28,2,10}*1120, {14,4,10}*1120
   9-fold covers : {7,2,45}*1260, {63,2,5}*1260, {21,2,15}*1260
   10-fold covers : {7,2,50}*1400, {14,2,25}*1400, {14,10,5}*1400, {35,2,10}*1400, {70,2,5}*1400
   11-fold covers : {7,2,55}*1540, {77,2,5}*1540
   12-fold covers : {7,2,60}*1680, {28,2,15}*1680, {21,2,20}*1680, {84,2,5}*1680, {14,6,10}*1680, {14,2,30}*1680, {42,2,10}*1680
   13-fold covers : {7,2,65}*1820, {91,2,5}*1820
   14-fold covers : {49,2,10}*1960, {98,2,5}*1960, {7,14,10}*1960, {7,2,70}*1960, {14,2,35}*1960
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope