Questions?
See the FAQ
or other info.

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

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

to this polytope