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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,2,6,10}*1680
if this polytope has a name.
Group : SmallGroup(1680,966)
Rank : 5
Schlafli Type : {7,2,6,10}
Number of vertices, edges, etc : 7, 7, 6, 30, 10
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 : {7,2,2,10}*560
   5-fold quotients : {7,2,6,2}*336
   6-fold quotients : {7,2,2,5}*280
   10-fold quotients : {7,2,3,2}*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 := (10,11)(14,15)(18,20)(19,21)(24,26)(25,27)(30,32)(31,33)(34,36)(35,37);;
s3 := ( 8,10)( 9,14)(12,19)(13,18)(16,25)(17,24)(20,21)(22,31)(23,30)(26,27)
(28,35)(29,34)(32,33)(36,37);;
s4 := ( 8,16)( 9,12)(10,24)(11,26)(13,28)(14,18)(15,20)(17,22)(19,34)(21,36)
(23,29)(25,30)(27,32)(31,35)(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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
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)(14,15)(18,20)(19,21)(24,26)(25,27)(30,32)(31,33)(34,36)
(35,37);
s3 := Sym(37)!( 8,10)( 9,14)(12,19)(13,18)(16,25)(17,24)(20,21)(22,31)(23,30)
(26,27)(28,35)(29,34)(32,33)(36,37);
s4 := Sym(37)!( 8,16)( 9,12)(10,24)(11,26)(13,28)(14,18)(15,20)(17,22)(19,34)
(21,36)(23,29)(25,30)(27,32)(31,35)(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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope