Polytope of Type {7,2,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,2,30}*840
if this polytope has a name.
Group : SmallGroup(840,171)
Rank : 4
Schlafli Type : {7,2,30}
Number of vertices, edges, etc : 7, 7, 30, 30
Order of s₀s₁s₂s₃ : 210
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {7,2,30,2} of size 1680
Vertex Figure Of :
   {2,7,2,30} of size 1680
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {7,2,15}*420
   3-fold quotients : {7,2,10}*280
   5-fold quotients : {7,2,6}*168
   6-fold quotients : {7,2,5}*140
   10-fold quotients : {7,2,3}*84
   15-fold quotients : {7,2,2}*56
Covers (Minimal Covers in Boldface) :
   2-fold covers : {7,2,60}*1680, {14,2,30}*1680
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)(18,21)(19,20)(22,23)(24,27)(25,26)(28,29)
(30,33)(31,32)(34,37)(35,36);;
s3 := ( 8,24)( 9,18)(10,16)(11,26)(12,14)(13,34)(15,20)(17,30)(19,28)(21,36)
(22,25)(23,35)(27,32)(29,31)(33,37);;
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*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(37)!(2,3)(4,5)(6,7);
s1 := Sym(37)!(1,2)(3,4)(5,6);
s2 := Sym(37)!(10,11)(12,13)(14,15)(16,17)(18,21)(19,20)(22,23)(24,27)(25,26)
(28,29)(30,33)(31,32)(34,37)(35,36);
s3 := Sym(37)!( 8,24)( 9,18)(10,16)(11,26)(12,14)(13,34)(15,20)(17,30)(19,28)
(21,36)(22,25)(23,35)(27,32)(29,31)(33,37);
poly := sub<Sym(37)|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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope