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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,8,14,2}*1792
if this polytope has a name.
Group : SmallGroup(1792,1083341)
Rank : 6
Schlafli Type : {2,2,8,14,2}
Number of vertices, edges, etc : 2, 2, 8, 56, 14, 2
Order of s0s1s2s3s4s5 : 56
Order of s0s1s2s3s4s5s4s3s2s1 : 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 : {2,2,4,14,2}*896
   4-fold quotients : {2,2,2,14,2}*448
   7-fold quotients : {2,2,8,2,2}*256
   8-fold quotients : {2,2,2,7,2}*224
   14-fold quotients : {2,2,4,2,2}*128
   28-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := (19,26)(20,27)(21,28)(22,29)(23,30)(24,31)(25,32)(33,47)(34,48)(35,49)
(36,50)(37,51)(38,52)(39,53)(40,54)(41,55)(42,56)(43,57)(44,58)(45,59)
(46,60);;
s3 := ( 5,33)( 6,39)( 7,38)( 8,37)( 9,36)(10,35)(11,34)(12,40)(13,46)(14,45)
(15,44)(16,43)(17,42)(18,41)(19,54)(20,60)(21,59)(22,58)(23,57)(24,56)(25,55)
(26,47)(27,53)(28,52)(29,51)(30,50)(31,49)(32,48);;
s4 := ( 5, 6)( 7,11)( 8,10)(12,13)(14,18)(15,17)(19,20)(21,25)(22,24)(26,27)
(28,32)(29,31)(33,34)(35,39)(36,38)(40,41)(42,46)(43,45)(47,48)(49,53)(50,52)
(54,55)(56,60)(57,59);;
s5 := (61,62);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, 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, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s2*s3*s4*s3*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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(62)!(1,2);
s1 := Sym(62)!(3,4);
s2 := Sym(62)!(19,26)(20,27)(21,28)(22,29)(23,30)(24,31)(25,32)(33,47)(34,48)
(35,49)(36,50)(37,51)(38,52)(39,53)(40,54)(41,55)(42,56)(43,57)(44,58)(45,59)
(46,60);
s3 := Sym(62)!( 5,33)( 6,39)( 7,38)( 8,37)( 9,36)(10,35)(11,34)(12,40)(13,46)
(14,45)(15,44)(16,43)(17,42)(18,41)(19,54)(20,60)(21,59)(22,58)(23,57)(24,56)
(25,55)(26,47)(27,53)(28,52)(29,51)(30,50)(31,49)(32,48);
s4 := Sym(62)!( 5, 6)( 7,11)( 8,10)(12,13)(14,18)(15,17)(19,20)(21,25)(22,24)
(26,27)(28,32)(29,31)(33,34)(35,39)(36,38)(40,41)(42,46)(43,45)(47,48)(49,53)
(50,52)(54,55)(56,60)(57,59);
s5 := Sym(62)!(61,62);
poly := sub<Sym(62)|s0,s1,s2,s3,s4,s5>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, 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, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, s2*s3*s4*s3*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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 >; 
 

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