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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,8,14}*1792
if this polytope has a name.
Group : SmallGroup(1792,1083341)
Rank : 6
Schlafli Type : {2,2,2,8,14}
Number of vertices, edges, etc : 2, 2, 2, 8, 56, 14
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 : {2,2,2,4,14}*896
   4-fold quotients : {2,2,2,2,14}*448
   7-fold quotients : {2,2,2,8,2}*256
   8-fold quotients : {2,2,2,2,7}*224
   14-fold quotients : {2,2,2,4,2}*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 := (5,6);;
s3 := (21,28)(22,29)(23,30)(24,31)(25,32)(26,33)(27,34)(35,49)(36,50)(37,51)
(38,52)(39,53)(40,54)(41,55)(42,56)(43,57)(44,58)(45,59)(46,60)(47,61)
(48,62);;
s4 := ( 7,35)( 8,41)( 9,40)(10,39)(11,38)(12,37)(13,36)(14,42)(15,48)(16,47)
(17,46)(18,45)(19,44)(20,43)(21,56)(22,62)(23,61)(24,60)(25,59)(26,58)(27,57)
(28,49)(29,55)(30,54)(31,53)(32,52)(33,51)(34,50);;
s5 := ( 7, 8)( 9,13)(10,12)(14,15)(16,20)(17,19)(21,22)(23,27)(24,26)(28,29)
(30,34)(31,33)(35,36)(37,41)(38,40)(42,43)(44,48)(45,47)(49,50)(51,55)(52,54)
(56,57)(58,62)(59,61);;
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, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(62)!(1,2);
s1 := Sym(62)!(3,4);
s2 := Sym(62)!(5,6);
s3 := Sym(62)!(21,28)(22,29)(23,30)(24,31)(25,32)(26,33)(27,34)(35,49)(36,50)
(37,51)(38,52)(39,53)(40,54)(41,55)(42,56)(43,57)(44,58)(45,59)(46,60)(47,61)
(48,62);
s4 := Sym(62)!( 7,35)( 8,41)( 9,40)(10,39)(11,38)(12,37)(13,36)(14,42)(15,48)
(16,47)(17,46)(18,45)(19,44)(20,43)(21,56)(22,62)(23,61)(24,60)(25,59)(26,58)
(27,57)(28,49)(29,55)(30,54)(31,53)(32,52)(33,51)(34,50);
s5 := Sym(62)!( 7, 8)( 9,13)(10,12)(14,15)(16,20)(17,19)(21,22)(23,27)(24,26)
(28,29)(30,34)(31,33)(35,36)(37,41)(38,40)(42,43)(44,48)(45,47)(49,50)(51,55)
(52,54)(56,57)(58,62)(59,61);
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, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >; 
 

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