Polytope of Type {2,3,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,6}*1176
if this polytope has a name.
Group : SmallGroup(1176,225)
Rank : 4
Schlafli Type : {2,3,6}
Number of vertices, edges, etc : 2, 49, 147, 98
Order of s₀s₁s₂s₃ : 14
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   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 := ( 4,24)( 5,45)( 6,17)( 7,38)( 8,10)( 9,31)(11,29)(12,50)(13,22)(14,43)
(16,36)(18,27)(19,48)(21,41)(23,34)(26,46)(28,39)(30,32)(33,51)(35,44)
(40,49);;
s2 := ( 4,45)( 5,38)( 6,31)( 7,24)( 8,17)( 9,10)(11,51)(12,44)(13,37)(14,30)
(15,23)(18,50)(19,43)(20,36)(21,29)(25,49)(26,42)(27,35)(32,48)(33,41)
(39,47);;
s3 := ( 3,25)( 5,32)( 6,11)( 7,39)( 8,18)( 9,46)(10,27)(12,34)(14,41)(15,20)
(16,48)(17,29)(19,36)(21,43)(23,50)(26,31)(28,38)(30,45)(35,40)(37,47)
(44,49);;
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(51)!(1,2);
s1 := Sym(51)!( 4,24)( 5,45)( 6,17)( 7,38)( 8,10)( 9,31)(11,29)(12,50)(13,22)
(14,43)(16,36)(18,27)(19,48)(21,41)(23,34)(26,46)(28,39)(30,32)(33,51)(35,44)
(40,49);
s2 := Sym(51)!( 4,45)( 5,38)( 6,31)( 7,24)( 8,17)( 9,10)(11,51)(12,44)(13,37)
(14,30)(15,23)(18,50)(19,43)(20,36)(21,29)(25,49)(26,42)(27,35)(32,48)(33,41)
(39,47);
s3 := Sym(51)!( 3,25)( 5,32)( 6,11)( 7,39)( 8,18)( 9,46)(10,27)(12,34)(14,41)
(15,20)(16,48)(17,29)(19,36)(21,43)(23,50)(26,31)(28,38)(30,45)(35,40)(37,47)
(44,49);
poly := sub<Sym(51)|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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 >;

to this polytope