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Polytope of Type {2,2,6,21}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,6,21}*1344
if this polytope has a name.
Group : SmallGroup(1344,11695)
Rank : 5
Schlafli Type : {2,2,6,21}
Number of vertices, edges, etc : 2, 2, 8, 84, 28
Order of s0s1s2s3s4 : 28
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) :
   7-fold quotients : {2,2,6,3}*192
   12-fold quotients : {2,2,2,7}*112
   14-fold quotients : {2,2,3,3}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)(10,11)(14,15)(18,19)(22,23)(26,27)(30,31);;
s3 := ( 7, 8)( 9,29)(10,30)(11,32)(12,31)(13,25)(14,26)(15,28)(16,27)(17,21)
(18,22)(19,24)(20,23);;
s4 := ( 5,12)( 6,10)( 7,11)( 8, 9)(13,32)(14,30)(15,31)(16,29)(17,28)(18,26)
(19,27)(20,25)(21,24);;
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*s1*s0*s1, 
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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, 
s3*s4*s3*s2*s4*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(32)!(1,2);
s1 := Sym(32)!(3,4);
s2 := Sym(32)!( 6, 7)(10,11)(14,15)(18,19)(22,23)(26,27)(30,31);
s3 := Sym(32)!( 7, 8)( 9,29)(10,30)(11,32)(12,31)(13,25)(14,26)(15,28)(16,27)
(17,21)(18,22)(19,24)(20,23);
s4 := Sym(32)!( 5,12)( 6,10)( 7,11)( 8, 9)(13,32)(14,30)(15,31)(16,29)(17,28)
(18,26)(19,27)(20,25)(21,24);
poly := sub<Sym(32)|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*s1*s0*s1, 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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, 
s3*s4*s3*s2*s4*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s3*s4 >; 
 

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