Questions?
See the FAQ
or other info.

Polytope of Type {2,18,6}

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

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