This tutorial is probably also available as a Jupyter notebook in the demo folder in the polymake source and on github.
Different versions of this tutorial: latest release, release 4.13, release 4.12, release 4.11, release 4.10, release 4.9, release 4.8, release 4.7, release 4.6, release 4.5, release 4.4, release 4.3, release 4.2, release 4.1, release 4.0, release 3.6, nightly master
Random Constructions
Random points on the unit sphere
The easiest way to randomly construct a polytope is by sampling points on the unit sphere. The following chooses 100 points on the units sphere in 3-space.
> $p1=rand_sphere(3,100); > print $p1->SIMPLICIAL; true
With probability one such polytopes are simplicial.
Random polytopes with are neither simplicial nor simple
> ($d,$m,$n) = (4,50,30); > $p1=rand_sphere($d,$m); > $p2=polarize($p1); > $p3=new Polytope(POINTS=>rand_vert($p2->VERTICES,$n)); > print $p3->SIMPLICIAL, " ", $p3->SIMPLE, "\n", $p3->F_VECTOR; false false 30 163 256 123