Polytope of Type {2,4,33,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,33,2}*1056
if this polytope has a name.
Group : SmallGroup(1056,1017)
Rank : 5
Schlafli Type : {2,4,33,2}
Number of vertices, edges, etc : 2, 4, 66, 33, 2
Order of s₀s₁s₂s₃s₄ : 66
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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) :
   11-fold quotients : {2,4,3,2}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)
(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)
(45,46);;
s2 := ( 4, 5)( 7,43)( 8,45)( 9,44)(10,46)(11,39)(12,41)(13,40)(14,42)(15,35)
(16,37)(17,36)(18,38)(19,31)(20,33)(21,32)(22,34)(23,27)(24,29)(25,28)
(26,30);;
s3 := ( 3, 7)( 4, 8)( 5,10)( 6, 9)(11,43)(12,44)(13,46)(14,45)(15,39)(16,40)
(17,42)(18,41)(19,35)(20,36)(21,38)(22,37)(23,31)(24,32)(25,34)(26,33)
(29,30);;
s4 := (47,48);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(48)!(1,2);
s1 := Sym(48)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)
(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)
(43,44)(45,46);
s2 := Sym(48)!( 4, 5)( 7,43)( 8,45)( 9,44)(10,46)(11,39)(12,41)(13,40)(14,42)
(15,35)(16,37)(17,36)(18,38)(19,31)(20,33)(21,32)(22,34)(23,27)(24,29)(25,28)
(26,30);
s3 := Sym(48)!( 3, 7)( 4, 8)( 5,10)( 6, 9)(11,43)(12,44)(13,46)(14,45)(15,39)
(16,40)(17,42)(18,41)(19,35)(20,36)(21,38)(22,37)(23,31)(24,32)(25,34)(26,33)
(29,30);
s4 := Sym(48)!(47,48);
poly := sub<Sym(48)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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