Polytope of Type {5,2,7}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,7}*140
if this polytope has a name.
Group : SmallGroup(140,7)
Rank : 4
Schlafli Type : {5,2,7}
Number of vertices, edges, etc : 5, 5, 7, 7
Order of s₀s₁s₂s₃ : 35
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,2,7,2} of size 280
   {5,2,7,14} of size 1960
Vertex Figure Of :
   {2,5,2,7} of size 280
   {3,5,2,7} of size 840
   {5,5,2,7} of size 840
   {10,5,2,7} of size 1400
   {4,5,2,7} of size 1680
   {6,5,2,7} of size 1680
   {3,5,2,7} of size 1680
   {5,5,2,7} of size 1680
   {6,5,2,7} of size 1680
   {6,5,2,7} of size 1680
   {10,5,2,7} of size 1680
   {10,5,2,7} of size 1680
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,2,14}*280, {10,2,7}*280
   3-fold covers : {15,2,7}*420, {5,2,21}*420
   4-fold covers : {20,2,7}*560, {5,2,28}*560, {10,2,14}*560
   5-fold covers : {25,2,7}*700, {5,2,35}*700
   6-fold covers : {15,2,14}*840, {30,2,7}*840, {5,2,42}*840, {10,2,21}*840
   7-fold covers : {5,2,49}*980, {35,2,7}*980
   8-fold covers : {40,2,7}*1120, {5,2,56}*1120, {20,2,14}*1120, {10,2,28}*1120, {10,4,14}*1120
   9-fold covers : {45,2,7}*1260, {5,2,63}*1260, {15,2,21}*1260
   10-fold covers : {25,2,14}*1400, {50,2,7}*1400, {5,10,14}*1400, {5,2,70}*1400, {10,2,35}*1400
   11-fold covers : {55,2,7}*1540, {5,2,77}*1540
   12-fold covers : {60,2,7}*1680, {15,2,28}*1680, {20,2,21}*1680, {5,2,84}*1680, {10,6,14}*1680, {30,2,14}*1680, {10,2,42}*1680
   13-fold covers : {65,2,7}*1820, {5,2,91}*1820
   14-fold covers : {5,2,98}*1960, {10,2,49}*1960, {10,14,7}*1960, {35,2,14}*1960, {70,2,7}*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);;
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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