pointmatrix = matrix([
[ 1, 1, 0, -1, -1, 0 ],
[ 0, 1, 1, 0, -1, -1 ],
[ 1, 1, 1, 1, 1, 1 ]
]);
pointmatrix = matrix(pointmatrix.rows()[0:2])
pointmatrix
[ 1 1 0 -1 -1 0] [ 0 1 1 0 -1 -1] [ 1 1 0 -1 -1 0] [ 0 1 1 0 -1 -1] |
pc = PointConfiguration(pointmatrix.columns()); pc
A point configuration in QQ^2 consisting of 6 points A point configuration in QQ^2 consisting of 6 points |
t = pc.triangulations_list()
t
[A triangulation in QQ^2 consisting of 4 simplices, A triangulation in QQ^2 consisting of 4 simplices, A triangulation in QQ^2 consisting of 4 simplices, A triangulation in QQ^2 consisting of 4 simplices, A triangulation in QQ^2 consisting of 4 simplices, A triangulation in QQ^2 consisting of 4 simplices, A triangulation in QQ^2 consisting of 4 simplices, A triangulation in QQ^2 consisting of 4 simplices, A triangulation in QQ^2 consisting of 4 simplices, A triangulation in QQ^2 consisting of 4 simplices, A triangulation in QQ^2 consisting of 4 simplices, A triangulation in QQ^2 consisting of 4 simplices, A triangulation in QQ^2 consisting of 4 simplices, A triangulation in QQ^2 consisting of 4 simplices] [A triangulation in QQ^2 consisting of 4 simplices, A triangulation in QQ^2 consisting of 4 simplices, A triangulation in QQ^2 consisting of 4 simplices, A triangulation in QQ^2 consisting of 4 simplices, A triangulation in QQ^2 consisting of 4 simplices, A triangulation in QQ^2 consisting of 4 simplices, A triangulation in QQ^2 consisting of 4 simplices, A triangulation in QQ^2 consisting of 4 simplices, A triangulation in QQ^2 consisting of 4 simplices, A triangulation in QQ^2 consisting of 4 simplices, A triangulation in QQ^2 consisting of 4 simplices, A triangulation in QQ^2 consisting of 4 simplices, A triangulation in QQ^2 consisting of 4 simplices, A triangulation in QQ^2 consisting of 4 simplices] |
# You can move the slider to see different triangulations
@interact
def show_triangulation(i=(1 .. len(t)+1)):
html('Triangulation number '+str(i)+' out of '+str(len(t)+1))
show( t[i-1].plot(axes=False) )
Click to the left again to hide and once more to show the dynamic interactive window |
secondarypolytope = pc.secondary_polytope()
secondarypolytope
A lattice polytope: 3-dimensional, 14 vertices. A lattice polytope: 3-dimensional, 14 vertices. |
plot = secondarypolytope.plot3d()
# the plot command gives nice live 3-d graphics in the web browser, but printing does not work
plot
|
|
plot.rotateZ(60*pi/180).show(viewer='tachyon')
|
p = Polyhedron( vertices=secondarypolytope.vertices().columns() ); p
A 3-dimensional polyhedron in QQ^6 defined as the convex hull of 14 vertices. A 3-dimensional polyhedron in QQ^6 defined as the convex hull of 14 vertices. |
edge_graph = p.graph()
edge_graph
Looped graph on 14 vertices Looped graph on 14 vertices |
edge_graph.show()
|
|
|
|