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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,2,4,4}*896
if this polytope has a name.
Group : SmallGroup(896,17749)
Rank : 5
Schlafli Type : {14,2,4,4}
Number of vertices, edges, etc : 14, 14, 4, 8, 4
Order of s0s1s2s3s4 : 28
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {14,2,4,4,2} of size 1792
Vertex Figure Of :
   {2,14,2,4,4} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {7,2,4,4}*448, {14,2,2,4}*448, {14,2,4,2}*448
   4-fold quotients : {7,2,2,4}*224, {7,2,4,2}*224, {14,2,2,2}*224
   7-fold quotients : {2,2,4,4}*128
   8-fold quotients : {7,2,2,2}*112
   14-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64
   28-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {14,4,4,4}*1792, {28,2,4,4}*1792, {14,2,4,8}*1792a, {14,2,8,4}*1792a, {14,2,4,8}*1792b, {14,2,8,4}*1792b, {14,2,4,4}*1792
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,14);;
s2 := (16,17)(18,20);;
s3 := (15,16)(17,19)(18,21)(20,22);;
s4 := (16,18)(17,20);;
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, 
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*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(22)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);
s1 := Sym(22)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,14);
s2 := Sym(22)!(16,17)(18,20);
s3 := Sym(22)!(15,16)(17,19)(18,21)(20,22);
s4 := Sym(22)!(16,18)(17,20);
poly := sub<Sym(22)|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, 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*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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