Polytope of Type {6,21,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,21,2}*672
if this polytope has a name.
Group : SmallGroup(672,1260)
Rank : 4
Schlafli Type : {6,21,2}
Number of vertices, edges, etc : 8, 84, 28, 2
Order of s₀s₁s₂s₃ : 28
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,21,2,2} of size 1344
Vertex Figure Of :
   {2,6,21,2} of size 1344
Quotients (Maximal Quotients in Boldface) :
   7-fold quotients : {6,3,2}*96
   12-fold quotients : {2,7,2}*56
   14-fold quotients : {3,3,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,21,2}*1344, {6,42,2}*1344
Permutation Representation (GAP) :

s0 := ( 2, 3)( 6, 7)(10,11)(14,15)(18,19)(22,23)(26,27);;
s1 := ( 3, 4)( 5,25)( 6,26)( 7,28)( 8,27)( 9,21)(10,22)(11,24)(12,23)(13,17)
(14,18)(15,20)(16,19);;
s2 := ( 1, 8)( 2, 6)( 3, 7)( 4, 5)( 9,28)(10,26)(11,27)(12,25)(13,24)(14,22)
(15,23)(16,21)(17,20);;
s3 := (29,30);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s0*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope