Polytope of Type {2,44,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,44,6}*1056b
if this polytope has a name.
Group : SmallGroup(1056,1015)
Rank : 4
Schlafli Type : {2,44,6}
Number of vertices, edges, etc : 2, 44, 132, 6
Order of s₀s₁s₂s₃ : 66
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) :
   11-fold quotients : {2,4,6}*96b
   22-fold quotients : {2,4,3}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope