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Polytope of Type {14,4,2,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,4,2,8}*1792
if this polytope has a name.
Group : SmallGroup(1792,1044755)
Rank : 5
Schlafli Type : {14,4,2,8}
Number of vertices, edges, etc : 14, 28, 4, 8, 8
Order of s0s1s2s3s4 : 56
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 : {14,4,2,4}*896, {14,2,2,8}*896
   4-fold quotients : {7,2,2,8}*448, {14,2,2,4}*448, {14,4,2,2}*448
   7-fold quotients : {2,4,2,8}*256
   8-fold quotients : {7,2,2,4}*224, {14,2,2,2}*224
   14-fold quotients : {2,4,2,4}*128, {2,2,2,8}*128
   16-fold quotients : {7,2,2,2}*112
   28-fold quotients : {2,2,2,4}*64, {2,4,2,2}*64
   56-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 6, 7)( 8, 9)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)
(25,26)(27,28);;
s1 := ( 1, 3)( 2,11)( 4, 8)( 5, 6)( 7,19)( 9,15)(10,17)(12,13)(14,25)(18,23)
(20,21)(22,26)(24,27);;
s2 := ( 1, 2)( 3, 6)( 4, 7)( 5,10)( 8,13)( 9,14)(11,17)(12,18)(15,21)(16,22)
(19,23)(20,24)(25,27)(26,28);;
s3 := (30,31)(32,33)(34,35);;
s4 := (29,30)(31,32)(33,34)(35,36);;
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, 
s3*s4*s3*s4*s3*s4*s3*s4*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(36)!( 3, 4)( 6, 7)( 8, 9)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)
(23,24)(25,26)(27,28);
s1 := Sym(36)!( 1, 3)( 2,11)( 4, 8)( 5, 6)( 7,19)( 9,15)(10,17)(12,13)(14,25)
(18,23)(20,21)(22,26)(24,27);
s2 := Sym(36)!( 1, 2)( 3, 6)( 4, 7)( 5,10)( 8,13)( 9,14)(11,17)(12,18)(15,21)
(16,22)(19,23)(20,24)(25,27)(26,28);
s3 := Sym(36)!(30,31)(32,33)(34,35);
s4 := Sym(36)!(29,30)(31,32)(33,34)(35,36);
poly := sub<Sym(36)|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, s3*s4*s3*s4*s3*s4*s3*s4*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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