Polytope of Type {12,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,3}*576
if this polytope has a name.
Group : SmallGroup(576,8653)
Rank : 3
Schlafli Type : {12,3}
Number of vertices, edges, etc : 96, 144, 24
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {12,3,2} of size 1152
Vertex Figure Of :
   {2,12,3} of size 1152
Quotients (Maximal Quotients in Boldface) :
   4-fold quotients : {6,3}*144, {12,3}*144
   12-fold quotients : {4,3}*48, {6,3}*48
   16-fold quotients : {6,3}*36
   24-fold quotients : {3,3}*24, {4,3}*24
   48-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,3}*1152b, {12,6}*1152g, {24,3}*1152b, {24,3}*1152c, {12,6}*1152j
   3-fold covers : {12,9}*1728, {12,3}*1728
Permutation Representation (GAP) :

s0 := ( 1, 9)( 2,11)( 3,10)( 4,12)( 5,13)( 6,15)( 7,14)( 8,16);;
s1 := ( 2, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(14,16);;
s2 := ( 1, 4)( 5,16)( 6,14)( 7,15)( 8,13)( 9,12);;
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, s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(16)!( 1, 9)( 2,11)( 3,10)( 4,12)( 5,13)( 6,15)( 7,14)( 8,16);
s1 := Sym(16)!( 2, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(14,16);
s2 := Sym(16)!( 1, 4)( 5,16)( 6,14)( 7,15)( 8,13)( 9,12);
poly := sub<Sym(16)|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, s1*s2*s1*s2*s1*s2, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*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 >;

References : None.
to this polytope