Polytope of Type {2,33,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,33,4}*528
if this polytope has a name.
Group : SmallGroup(528,162)
Rank : 4
Schlafli Type : {2,33,4}
Number of vertices, edges, etc : 2, 33, 66, 4
Order of s₀s₁s₂s₃ : 66
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,33,4,2} of size 1056
Vertex Figure Of :
   {2,2,33,4} of size 1056
   {3,2,33,4} of size 1584
Quotients (Maximal Quotients in Boldface) :
   11-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,33,4}*1056, {2,66,4}*1056b, {2,66,4}*1056c
   3-fold covers : {2,99,4}*1584, {6,33,4}*1584
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope