Polytope of Type {7,2,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,2,20}*560
if this polytope has a name.
Group : SmallGroup(560,120)
Rank : 4
Schlafli Type : {7,2,20}
Number of vertices, edges, etc : 7, 7, 20, 20
Order of s₀s₁s₂s₃ : 140
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {7,2,20,2} of size 1120
Vertex Figure Of :
   {2,7,2,20} of size 1120
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {7,2,10}*280
   4-fold quotients : {7,2,5}*140
   5-fold quotients : {7,2,4}*112
   10-fold quotients : {7,2,2}*56
Covers (Minimal Covers in Boldface) :
   2-fold covers : {7,2,40}*1120, {14,2,20}*1120
   3-fold covers : {7,2,60}*1680, {21,2,20}*1680
Permutation Representation (GAP) :

s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6);;
s2 := ( 9,10)(11,12)(14,17)(15,16)(18,19)(20,21)(22,25)(23,24)(26,27);;
s3 := ( 8,14)( 9,11)(10,20)(12,22)(13,16)(15,18)(17,26)(19,23)(21,24)(25,27);;
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*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(27)!(2,3)(4,5)(6,7);
s1 := Sym(27)!(1,2)(3,4)(5,6);
s2 := Sym(27)!( 9,10)(11,12)(14,17)(15,16)(18,19)(20,21)(22,25)(23,24)(26,27);
s3 := Sym(27)!( 8,14)( 9,11)(10,20)(12,22)(13,16)(15,18)(17,26)(19,23)(21,24)
(25,27);
poly := sub<Sym(27)|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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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