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Polytope of Type {2,28,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,28,6,2}*1344b
if this polytope has a name.
Group : SmallGroup(1344,11695)
Rank : 5
Schlafli Type : {2,28,6,2}
Number of vertices, edges, etc : 2, 28, 84, 6, 2
Order of s0s1s2s3s4 : 42
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-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 : {2,4,6,2}*192b
   14-fold quotients : {2,4,3,2}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3, 5)( 4, 6)( 7,29)( 8,30)( 9,27)(10,28)(11,25)(12,26)(13,23)(14,24)
(15,21)(16,22)(17,19)(18,20);;
s2 := ( 3, 7)( 4, 9)( 5, 8)( 6,10)(11,27)(12,29)(13,28)(14,30)(15,23)(16,25)
(17,24)(18,26)(20,21);;
s3 := ( 4, 6)( 8,10)(12,14)(16,18)(20,22)(24,26)(28,30);;
s4 := (31,32);;
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, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2, 
s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(32)!(1,2);
s1 := Sym(32)!( 3, 5)( 4, 6)( 7,29)( 8,30)( 9,27)(10,28)(11,25)(12,26)(13,23)
(14,24)(15,21)(16,22)(17,19)(18,20);
s2 := Sym(32)!( 3, 7)( 4, 9)( 5, 8)( 6,10)(11,27)(12,29)(13,28)(14,30)(15,23)
(16,25)(17,24)(18,26)(20,21);
s3 := Sym(32)!( 4, 6)( 8,10)(12,14)(16,18)(20,22)(24,26)(28,30);
s4 := Sym(32)!(31,32);
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2, 
s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1 >; 
 

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