Polytope of Type {2,4,7}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,7}*1792
if this polytope has a name.
Group : SmallGroup(1792,1083553)
Rank : 4
Schlafli Type : {2,4,7}
Number of vertices, edges, etc : 2, 64, 224, 112
Order of s₀s₁s₂s₃ : 14
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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 := (1,2);;
s1 := ( 3,39)( 4,40)( 5,41)( 6,42)( 7,35)( 8,36)( 9,37)(10,38)(11,47)(12,48)
(13,49)(14,50)(15,43)(16,44)(17,45)(18,46)(19,55)(20,56)(21,57)(22,58)(23,51)
(24,52)(25,53)(26,54)(27,63)(28,64)(29,65)(30,66)(31,59)(32,60)(33,61)
(34,62);;
s2 := ( 4,51)( 5,19)( 6,35)( 7,27)( 8,43)( 9,11)(10,59)(12,57)(13,25)(14,41)
(15,33)(16,49)(18,65)(20,53)(22,37)(23,29)(24,45)(26,61)(28,55)(30,39)(32,47)
(34,63)(36,54)(40,46)(42,62)(44,56)(50,64)(58,60);;
s3 := ( 4,59)( 5,51)( 6,11)( 7,35)( 8,27)( 9,19)(10,43)(12,62)(13,54)(15,38)
(16,30)(17,22)(18,46)(20,65)(21,57)(23,41)(24,33)(26,49)(28,64)(29,56)(31,40)
(34,48)(36,63)(37,55)(42,47)(44,66)(45,58)(52,61);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(66)!(1,2);
s1 := Sym(66)!( 3,39)( 4,40)( 5,41)( 6,42)( 7,35)( 8,36)( 9,37)(10,38)(11,47)
(12,48)(13,49)(14,50)(15,43)(16,44)(17,45)(18,46)(19,55)(20,56)(21,57)(22,58)
(23,51)(24,52)(25,53)(26,54)(27,63)(28,64)(29,65)(30,66)(31,59)(32,60)(33,61)
(34,62);
s2 := Sym(66)!( 4,51)( 5,19)( 6,35)( 7,27)( 8,43)( 9,11)(10,59)(12,57)(13,25)
(14,41)(15,33)(16,49)(18,65)(20,53)(22,37)(23,29)(24,45)(26,61)(28,55)(30,39)
(32,47)(34,63)(36,54)(40,46)(42,62)(44,56)(50,64)(58,60);
s3 := Sym(66)!( 4,59)( 5,51)( 6,11)( 7,35)( 8,27)( 9,19)(10,43)(12,62)(13,54)
(15,38)(16,30)(17,22)(18,46)(20,65)(21,57)(23,41)(24,33)(26,49)(28,64)(29,56)
(31,40)(34,48)(36,63)(37,55)(42,47)(44,66)(45,58)(52,61);
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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3 >;

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