Polytope of Type {2,3,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,6}*1944
if this polytope has a name.
Group : SmallGroup(1944,956)
Rank : 4
Schlafli Type : {2,3,6}
Number of vertices, edges, etc : 2, 81, 243, 162
Order of s₀s₁s₂s₃ : 18
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) :
   3-fold quotients : {2,3,6}*648
   9-fold quotients : {2,3,6}*216
   27-fold quotients : {2,3,6}*72
   81-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (12,21)(13,22)(14,23)(15,26)(16,24)(17,25)(18,28)(19,29)(20,27);;
s2 := ( 3,15)( 4,16)( 5,17)( 6,18)( 7,19)( 8,20)( 9,14)(10,12)(11,13);;
s3 := ( 4, 5)( 6,10)( 7, 9)( 8,11)(12,21)(13,23)(14,22)(15,29)(16,28)(17,27)
(18,24)(19,26)(20,25);;
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*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(29)!(1,2);
s1 := Sym(29)!(12,21)(13,22)(14,23)(15,26)(16,24)(17,25)(18,28)(19,29)(20,27);
s2 := Sym(29)!( 3,15)( 4,16)( 5,17)( 6,18)( 7,19)( 8,20)( 9,14)(10,12)(11,13);
s3 := Sym(29)!( 4, 5)( 6,10)( 7, 9)( 8,11)(12,21)(13,23)(14,22)(15,29)(16,28)
(17,27)(18,24)(19,26)(20,25);
poly := sub<Sym(29)|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*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 >;

to this polytope