Polytope of Type {2,6,21}

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

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

Permutation Representation (Magma) :

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

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