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Polytope of Type {7,7,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,7,2}*1792
if this polytope has a name.
Group : SmallGroup(1792,1083553)
Rank : 4
Schlafli Type : {7,7,2}
Number of vertices, edges, etc : 64, 224, 64, 2
Order of s0s1s2s3 : 4
Order of s0s1s2s3s2s1 : 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) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2,49)( 3,17)( 4,33)( 5,25)( 6,41)( 7, 9)( 8,57)(10,55)(11,23)(12,39)
(13,31)(14,47)(16,63)(18,51)(20,35)(21,27)(22,43)(24,59)(26,53)(28,37)(30,45)
(32,61)(34,52)(38,44)(40,60)(42,54)(48,62)(56,58);;
s1 := ( 2,33)( 3,25)( 4,57)( 5,49)( 6,17)( 7,41)( 8, 9)(10,40)(11,32)(12,64)
(13,56)(14,24)(15,48)(18,38)(19,30)(20,62)(21,54)(23,46)(26,35)(28,59)(29,51)
(31,43)(36,58)(37,50)(39,42)(44,63)(45,55)(52,61);;
s2 := ( 1,19)( 2,35)( 4,51)( 5,11)( 6,59)( 7,27)( 8,43)( 9,21)(10,37)(12,53)
(14,61)(15,29)(16,45)(18,33)(20,49)(22,57)(23,25)(24,41)(26,39)(28,55)(30,63)
(32,47)(36,50)(38,58)(40,42)(44,56)(46,64)(54,60);;
s3 := (65,66);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*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, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(66)!( 2,49)( 3,17)( 4,33)( 5,25)( 6,41)( 7, 9)( 8,57)(10,55)(11,23)
(12,39)(13,31)(14,47)(16,63)(18,51)(20,35)(21,27)(22,43)(24,59)(26,53)(28,37)
(30,45)(32,61)(34,52)(38,44)(40,60)(42,54)(48,62)(56,58);
s1 := Sym(66)!( 2,33)( 3,25)( 4,57)( 5,49)( 6,17)( 7,41)( 8, 9)(10,40)(11,32)
(12,64)(13,56)(14,24)(15,48)(18,38)(19,30)(20,62)(21,54)(23,46)(26,35)(28,59)
(29,51)(31,43)(36,58)(37,50)(39,42)(44,63)(45,55)(52,61);
s2 := Sym(66)!( 1,19)( 2,35)( 4,51)( 5,11)( 6,59)( 7,27)( 8,43)( 9,21)(10,37)
(12,53)(14,61)(15,29)(16,45)(18,33)(20,49)(22,57)(23,25)(24,41)(26,39)(28,55)
(30,63)(32,47)(36,50)(38,58)(40,42)(44,56)(46,64)(54,60);
s3 := Sym(66)!(65,66);
poly := sub<Sym(66)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*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, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1 >; 
 

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