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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,14,2,4}*1792
if this polytope has a name.
Group : SmallGroup(1792,1044755)
Rank : 5
Schlafli Type : {8,14,2,4}
Number of vertices, edges, etc : 8, 56, 14, 4, 4
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 : {4,14,2,4}*896, {8,14,2,2}*896
   4-fold quotients : {2,14,2,4}*448, {4,14,2,2}*448
   7-fold quotients : {8,2,2,4}*256
   8-fold quotients : {2,7,2,4}*224, {2,14,2,2}*224
   14-fold quotients : {4,2,2,4}*128, {8,2,2,2}*128
   16-fold quotients : {2,7,2,2}*112
   28-fold quotients : {2,2,2,4}*64, {4,2,2,2}*64
   56-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (15,22)(16,23)(17,24)(18,25)(19,26)(20,27)(21,28)(29,43)(30,44)(31,45)
(32,46)(33,47)(34,48)(35,49)(36,50)(37,51)(38,52)(39,53)(40,54)(41,55)
(42,56);;
s1 := ( 1,29)( 2,35)( 3,34)( 4,33)( 5,32)( 6,31)( 7,30)( 8,36)( 9,42)(10,41)
(11,40)(12,39)(13,38)(14,37)(15,50)(16,56)(17,55)(18,54)(19,53)(20,52)(21,51)
(22,43)(23,49)(24,48)(25,47)(26,46)(27,45)(28,44);;
s2 := ( 1, 2)( 3, 7)( 4, 6)( 8, 9)(10,14)(11,13)(15,16)(17,21)(18,20)(22,23)
(24,28)(25,27)(29,30)(31,35)(32,34)(36,37)(38,42)(39,41)(43,44)(45,49)(46,48)
(50,51)(52,56)(53,55);;
s3 := (58,59);;
s4 := (57,58)(59,60);;
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, s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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(60)!(15,22)(16,23)(17,24)(18,25)(19,26)(20,27)(21,28)(29,43)(30,44)
(31,45)(32,46)(33,47)(34,48)(35,49)(36,50)(37,51)(38,52)(39,53)(40,54)(41,55)
(42,56);
s1 := Sym(60)!( 1,29)( 2,35)( 3,34)( 4,33)( 5,32)( 6,31)( 7,30)( 8,36)( 9,42)
(10,41)(11,40)(12,39)(13,38)(14,37)(15,50)(16,56)(17,55)(18,54)(19,53)(20,52)
(21,51)(22,43)(23,49)(24,48)(25,47)(26,46)(27,45)(28,44);
s2 := Sym(60)!( 1, 2)( 3, 7)( 4, 6)( 8, 9)(10,14)(11,13)(15,16)(17,21)(18,20)
(22,23)(24,28)(25,27)(29,30)(31,35)(32,34)(36,37)(38,42)(39,41)(43,44)(45,49)
(46,48)(50,51)(52,56)(53,55);
s3 := Sym(60)!(58,59);
s4 := Sym(60)!(57,58)(59,60);
poly := sub<Sym(60)|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, 
s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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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