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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}*1296b
if this polytope has a name.
Group : SmallGroup(1296,1788)
Rank : 3
Schlafli Type : {12,9}
Number of vertices, edges, etc : 72, 324, 54
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {12,3}*432
   4-fold quotients : {6,9}*324c
   9-fold quotients : {12,3}*144
   12-fold quotients : {6,3}*108
   27-fold quotients : {4,3}*48
   36-fold quotients : {6,3}*36
   54-fold quotients : {4,3}*24
   108-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,27)(14,28)(15,25)(16,26)
(17,31)(18,32)(19,29)(20,30)(21,35)(22,36)(23,33)(24,34);;
s1 := ( 1,13)( 2,14)( 3,16)( 4,15)( 5,21)( 6,22)( 7,24)( 8,23)( 9,17)(10,18)
(11,20)(12,19)(27,28)(29,33)(30,34)(31,36)(32,35);;
s2 := ( 2, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(13,29)(14,32)(15,31)(16,30)(17,25)
(18,28)(19,27)(20,26)(21,33)(22,36)(23,35)(24,34);;
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*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*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(36)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,27)(14,28)(15,25)
(16,26)(17,31)(18,32)(19,29)(20,30)(21,35)(22,36)(23,33)(24,34);
s1 := Sym(36)!( 1,13)( 2,14)( 3,16)( 4,15)( 5,21)( 6,22)( 7,24)( 8,23)( 9,17)
(10,18)(11,20)(12,19)(27,28)(29,33)(30,34)(31,36)(32,35);
s2 := Sym(36)!( 2, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(13,29)(14,32)(15,31)(16,30)
(17,25)(18,28)(19,27)(20,26)(21,33)(22,36)(23,35)(24,34);
poly := sub<Sym(36)|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*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*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