Polytope of Type {3,12,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,12,3}*1728
if this polytope has a name.
Group : SmallGroup(1728,46101)
Rank : 4
Schlafli Type : {3,12,3}
Number of vertices, edges, etc : 12, 144, 144, 12
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 12
Special Properties :
   Orientable
   Self-Dual
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 : {3,4,3}*576
   16-fold quotients : {3,6,3}*108
   48-fold quotients : {3,2,3}*36
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11)(13,21)(14,23)(15,22)(16,24)(18,19)
(25,33)(26,36)(27,35)(28,34)(30,32);;
s1 := ( 1, 9)( 2,12)( 3,11)( 4,10)( 6, 8)(15,16)(17,21)(18,22)(19,24)(20,23)
(25,33)(26,35)(27,34)(28,36)(30,31);;
s2 := ( 5, 9)( 6,10)( 7,11)( 8,12)(13,35)(14,34)(15,36)(16,33)(17,31)(18,30)
(19,32)(20,29)(21,27)(22,26)(23,28)(24,25);;
s3 := ( 1,17)( 2,20)( 3,18)( 4,19)( 5,13)( 6,16)( 7,14)( 8,15)( 9,21)(10,24)
(11,22)(12,23)(25,33)(26,34)(27,35)(28,36);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1, 
s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s0*s2*s1*s0*s2*s1*s3*s2*s3*s1*s2*s0*s1*s3*s2*s3*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(36)!( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11)(13,21)(14,23)(15,22)(16,24)
(18,19)(25,33)(26,36)(27,35)(28,34)(30,32);
s1 := Sym(36)!( 1, 9)( 2,12)( 3,11)( 4,10)( 6, 8)(15,16)(17,21)(18,22)(19,24)
(20,23)(25,33)(26,35)(27,34)(28,36)(30,31);
s2 := Sym(36)!( 5, 9)( 6,10)( 7,11)( 8,12)(13,35)(14,34)(15,36)(16,33)(17,31)
(18,30)(19,32)(20,29)(21,27)(22,26)(23,28)(24,25);
s3 := Sym(36)!( 1,17)( 2,20)( 3,18)( 4,19)( 5,13)( 6,16)( 7,14)( 8,15)( 9,21)
(10,24)(11,22)(12,23)(25,33)(26,34)(27,35)(28,36);
poly := sub<Sym(36)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1, 
s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s0*s2*s1*s0*s2*s1*s3*s2*s3*s1*s2*s0*s1*s3*s2*s3*s1*s2*s0*s1*s2*s0*s1 >;

References : None.
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