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Polytope of Type {4,14,2,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,14,2,6}*1344
if this polytope has a name.
Group : SmallGroup(1344,11527)
Rank : 5
Schlafli Type : {4,14,2,6}
Number of vertices, edges, etc : 4, 28, 14, 6, 6
Order of s0s1s2s3s4 : 84
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) :
   2-fold quotients : {4,14,2,3}*672, {2,14,2,6}*672
   3-fold quotients : {4,14,2,2}*448
   4-fold quotients : {2,7,2,6}*336, {2,14,2,3}*336
   6-fold quotients : {2,14,2,2}*224
   7-fold quotients : {4,2,2,6}*192
   8-fold quotients : {2,7,2,3}*168
   12-fold quotients : {2,7,2,2}*112
   14-fold quotients : {4,2,2,3}*96, {2,2,2,6}*96
   21-fold quotients : {4,2,2,2}*64
   28-fold quotients : {2,2,2,3}*48
   42-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 5)( 6,11)( 7,12)(13,19)(14,20)(21,25)(22,26);;
s1 := ( 1, 2)( 3, 7)( 4, 6)( 5,10)( 8,14)( 9,13)(11,18)(12,17)(15,22)(16,21)
(19,24)(20,23)(25,28)(26,27);;
s2 := ( 1, 3)( 2, 6)( 4, 8)( 5,11)( 7,13)( 9,15)(10,17)(12,19)(14,21)(18,23)
(20,25)(24,27);;
s3 := (31,32)(33,34);;
s4 := (29,33)(30,31)(32,34);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(34)!( 2, 5)( 6,11)( 7,12)(13,19)(14,20)(21,25)(22,26);
s1 := Sym(34)!( 1, 2)( 3, 7)( 4, 6)( 5,10)( 8,14)( 9,13)(11,18)(12,17)(15,22)
(16,21)(19,24)(20,23)(25,28)(26,27);
s2 := Sym(34)!( 1, 3)( 2, 6)( 4, 8)( 5,11)( 7,13)( 9,15)(10,17)(12,19)(14,21)
(18,23)(20,25)(24,27);
s3 := Sym(34)!(31,32)(33,34);
s4 := Sym(34)!(29,33)(30,31)(32,34);
poly := sub<Sym(34)|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*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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