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Polytope of Type {12,9}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,9}*648b
if this polytope has a name.
Group : SmallGroup(648,703)
Rank : 3
Schlafli Type : {12,9}
Number of vertices, edges, etc : 36, 162, 27
Order of s₀s₁s₂ : 3
Order of s₀s₁s₂s₁ : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {12,9,2} of size 1296
Vertex Figure Of :
   {2,12,9} of size 1296
Quotients (Maximal Quotients in Boldface) :
   27-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,9}*1296f, {12,18}*1296n, {12,18}*1296p
   3-fold covers : {12,9}*1944c
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope