Polytope of Type {7,2,10,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,2,10,6}*1680
if this polytope has a name.
Group : SmallGroup(1680,966)
Rank : 5
Schlafli Type : {7,2,10,6}
Number of vertices, edges, etc : 7, 7, 10, 30, 6
Order of s₀s₁s₂s₃s₄ : 210
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {7,2,10,2}*560
   5-fold quotients : {7,2,2,6}*336
   6-fold quotients : {7,2,5,2}*280
   10-fold quotients : {7,2,2,3}*168
   15-fold quotients : {7,2,2,2}*112
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6);;
s2 := (12,13)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)
(34,35)(36,37);;
s3 := ( 8,12)( 9,16)(10,20)(11,18)(13,22)(14,26)(15,24)(17,28)(19,32)(21,30)
(25,36)(27,34)(31,33)(35,37);;
s4 := ( 8,14)( 9,10)(11,15)(12,24)(13,25)(16,18)(17,19)(20,26)(21,27)(22,34)
(23,35)(28,30)(29,31)(32,36)(33,37);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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 ];;
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)!(12,13)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)
(32,33)(34,35)(36,37);
s3 := Sym(37)!( 8,12)( 9,16)(10,20)(11,18)(13,22)(14,26)(15,24)(17,28)(19,32)
(21,30)(25,36)(27,34)(31,33)(35,37);
s4 := Sym(37)!( 8,14)( 9,10)(11,15)(12,24)(13,25)(16,18)(17,19)(20,26)(21,27)
(22,34)(23,35)(28,30)(29,31)(32,36)(33,37);
poly := sub<Sym(37)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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 >;

to this polytope