Polytope of Type {2,6,44}

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

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

Permutation Representation (Magma) :

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

to this polytope