
D.13.1.6 triangulations
Procedure from library polymake.lib (see polymake_lib).
 Usage:
 triangulations(polygon[,#]); list polygon, list #
 Assume:
 polygon is a list of integer vectors of the same size representing
the affine coordinates of the lattice points
 Purpose:
 the procedure considers the marked polytope given as the convex hull of
the lattice points and with these lattice points as markings; it then
computes all possible triangulations of this marked polytope
 Return:
 list, each entry corresponds to one triangulation and the ith entry is
itself a list of integer vectors of size three, where each integer
vector defines one triangle in the triangulation by telling which
points of the input are the vertices of the triangle
 Note:
  the procedure calls for its computations the program points2triangs
from the program topcom by Joerg Rambau, Universitaet Bayreuth; it
therefore is necessary that this program is installed in order to use
this procedure; see
http://www.unibayreuth.de/departments/wirtschaftsmathematik/rambau/TOPCOM
 if you only want to have the regular triangulations the procedure should
be called with the string 'regular' as optional argument
 the procedure creates the files /tmp/triangulationsinput and
/tmp/triangulationsoutput;
the former is used as input for points2triangs and the latter is its
output containing the triangulations of corresponding to points in the
format of points2triangs; if you wish to use this for further
computations with topcom, you have to call the procedure with the
string 'keepfiles' as optional argument
 note that an integer i in an integer vector representing a triangle
refers to the ith lattice point, i.e. polygon[i]; this convention is
different from TOPCOM's convention, where i would refer to the i1st
lattice point
Example:
 LIB "polymake.lib";
// the lattice points of the unit square in the plane
list polygon=intvec(0,0),intvec(0,1),intvec(1,0),intvec(1,1);
// the triangulations of this lattice point configuration are computed
list triang=triangulations(polygon);
triang;

