Polytope of Type {18,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,6}*972e
Also Known As : {18,6}₃. if this polytope has another name.
Group : SmallGroup(972,115)
Rank : 3
Schlafli Type : {18,6}
Number of vertices, edges, etc : 81, 243, 27
Order of s₀s₁s₂ : 3
Order of s₀s₁s₂s₁ : 18
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {18,6,2} of size 1944
Vertex Figure Of :
   {2,18,6} of size 1944
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {18,6}*324c
   9-fold quotients : {6,6}*108
Covers (Minimal Covers in Boldface) :
   2-fold covers : {18,6}*1944l
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s0*s1*s2*s0*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s0*s1*s2*s0*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope