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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,14,8}*1792
if this polytope has a name.
Group : SmallGroup(1792,1083341)
Rank : 6
Schlafli Type : {2,2,2,14,8}
Number of vertices, edges, etc : 2, 2, 2, 14, 56, 8
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 : {2,2,2,14,4}*896
   4-fold quotients : {2,2,2,14,2}*448
   7-fold quotients : {2,2,2,2,8}*256
   8-fold quotients : {2,2,2,7,2}*224
   14-fold quotients : {2,2,2,2,4}*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 := (5,6);;
s3 := ( 8,13)( 9,12)(10,11)(15,20)(16,19)(17,18)(22,27)(23,26)(24,25)(29,34)
(30,33)(31,32)(36,41)(37,40)(38,39)(43,48)(44,47)(45,46)(50,55)(51,54)(52,53)
(57,62)(58,61)(59,60);;
s4 := ( 7, 8)( 9,13)(10,12)(14,15)(16,20)(17,19)(21,29)(22,28)(23,34)(24,33)
(25,32)(26,31)(27,30)(35,50)(36,49)(37,55)(38,54)(39,53)(40,52)(41,51)(42,57)
(43,56)(44,62)(45,61)(46,60)(47,59)(48,58);;
s5 := ( 7,35)( 8,36)( 9,37)(10,38)(11,39)(12,40)(13,41)(14,42)(15,43)(16,44)
(17,45)(18,46)(19,47)(20,48)(21,56)(22,57)(23,58)(24,59)(25,60)(26,61)(27,62)
(28,49)(29,50)(30,51)(31,52)(32,53)(33,54)(34,55);;
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, s2*s3*s2*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, s3*s4*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, 
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)!(5,6);
s3 := Sym(62)!( 8,13)( 9,12)(10,11)(15,20)(16,19)(17,18)(22,27)(23,26)(24,25)
(29,34)(30,33)(31,32)(36,41)(37,40)(38,39)(43,48)(44,47)(45,46)(50,55)(51,54)
(52,53)(57,62)(58,61)(59,60);
s4 := Sym(62)!( 7, 8)( 9,13)(10,12)(14,15)(16,20)(17,19)(21,29)(22,28)(23,34)
(24,33)(25,32)(26,31)(27,30)(35,50)(36,49)(37,55)(38,54)(39,53)(40,52)(41,51)
(42,57)(43,56)(44,62)(45,61)(46,60)(47,59)(48,58);
s5 := Sym(62)!( 7,35)( 8,36)( 9,37)(10,38)(11,39)(12,40)(13,41)(14,42)(15,43)
(16,44)(17,45)(18,46)(19,47)(20,48)(21,56)(22,57)(23,58)(24,59)(25,60)(26,61)
(27,62)(28,49)(29,50)(30,51)(31,52)(32,53)(33,54)(34,55);
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, 
s2*s3*s2*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, s3*s4*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, 
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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