Polytope of Type {21,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {21,6,2}*672
if this polytope has a name.
Group : SmallGroup(672,1260)
Rank : 4
Schlafli Type : {21,6,2}
Number of vertices, edges, etc : 28, 84, 8, 2
Order of s0s1s2s3 : 28
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {21,6,2,2} of size 1344
Vertex Figure Of :
   {2,21,6,2} of size 1344
Quotients (Maximal Quotients in Boldface) :
   7-fold quotients : {3,6,2}*96
   12-fold quotients : {7,2,2}*56
   14-fold quotients : {3,3,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {21,12,2}*1344, {21,6,4}*1344, {42,6,2}*1344
Permutation Representation (GAP) :
s0 := ( 2, 3)( 5,25)( 6,27)( 7,26)( 8,28)( 9,21)(10,23)(11,22)(12,24)(13,17)
(14,19)(15,18)(16,20);;
s1 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 9,25)(10,26)(11,28)(12,27)(13,21)(14,22)
(15,24)(16,23)(19,20);;
s2 := ( 1, 4)( 5, 8)( 9,12)(13,16)(17,20)(21,24)(25,28);;
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*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(30)!( 2, 3)( 5,25)( 6,27)( 7,26)( 8,28)( 9,21)(10,23)(11,22)(12,24)
(13,17)(14,19)(15,18)(16,20);
s1 := Sym(30)!( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 9,25)(10,26)(11,28)(12,27)(13,21)
(14,22)(15,24)(16,23)(19,20);
s2 := Sym(30)!( 1, 4)( 5, 8)( 9,12)(13,16)(17,20)(21,24)(25,28);
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*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >; 
 

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