Polytope of Type {5,2,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,14}*280
if this polytope has a name.
Group : SmallGroup(280,36)
Rank : 4
Schlafli Type : {5,2,14}
Number of vertices, edges, etc : 5, 5, 14, 14
Order of s₀s₁s₂s₃ : 70
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,2,14,2} of size 560
   {5,2,14,4} of size 1120
   {5,2,14,6} of size 1680
   {5,2,14,7} of size 1960
Vertex Figure Of :
   {2,5,2,14} of size 560
   {3,5,2,14} of size 1680
   {5,5,2,14} of size 1680
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,2,7}*140
   7-fold quotients : {5,2,2}*40
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,2,28}*560, {10,2,14}*560
   3-fold covers : {15,2,14}*840, {5,2,42}*840
   4-fold covers : {5,2,56}*1120, {20,2,14}*1120, {10,2,28}*1120, {10,4,14}*1120
   5-fold covers : {25,2,14}*1400, {5,10,14}*1400, {5,2,70}*1400
   6-fold covers : {15,2,28}*1680, {5,2,84}*1680, {10,6,14}*1680, {30,2,14}*1680, {10,2,42}*1680
   7-fold covers : {5,2,98}*1960, {35,2,14}*1960
Permutation Representation (GAP) :

s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := ( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19);;
s3 := ( 6,10)( 7, 8)( 9,14)(11,12)(13,18)(15,16)(17,19);;
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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(19)!(2,3)(4,5);
s1 := Sym(19)!(1,2)(3,4);
s2 := Sym(19)!( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19);
s3 := Sym(19)!( 6,10)( 7, 8)( 9,14)(11,12)(13,18)(15,16)(17,19);
poly := sub<Sym(19)|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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope