Polytope of Type {7,2,8,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,2,8,6}*1344
if this polytope has a name.
Group : SmallGroup(1344,8561)
Rank : 5
Schlafli Type : {7,2,8,6}
Number of vertices, edges, etc : 7, 7, 8, 24, 6
Order of s₀s₁s₂s₃s₄ : 168
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) :
   2-fold quotients : {7,2,4,6}*672a
   3-fold quotients : {7,2,8,2}*448
   4-fold quotients : {7,2,2,6}*336
   6-fold quotients : {7,2,4,2}*224
   8-fold quotients : {7,2,2,3}*168
   12-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 := ( 9,12)(13,16)(14,17)(15,18)(19,22)(20,23)(21,24)(25,28)(26,29);;
s3 := ( 8, 9)(10,14)(11,13)(12,15)(16,20)(17,19)(18,21)(22,26)(23,25)(24,27)
(28,31)(29,30);;
s4 := ( 8,10)( 9,13)(12,16)(15,19)(18,22)(21,25)(24,28)(27,30);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(31)!(2,3)(4,5)(6,7);
s1 := Sym(31)!(1,2)(3,4)(5,6);
s2 := Sym(31)!( 9,12)(13,16)(14,17)(15,18)(19,22)(20,23)(21,24)(25,28)(26,29);
s3 := Sym(31)!( 8, 9)(10,14)(11,13)(12,15)(16,20)(17,19)(18,21)(22,26)(23,25)
(24,27)(28,31)(29,30);
s4 := Sym(31)!( 8,10)( 9,13)(12,16)(15,19)(18,22)(21,25)(24,28)(27,30);
poly := sub<Sym(31)|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 >;

to this polytope