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.

polytope > $p1=rand_sphere(3,100); polytope > print $p1->SIMPLICIAL; 1

With probability one such polytopes are simplicial.

polytope > ($d,$m,$n) = (4,50,30); polytope > $p1=rand_sphere($d,$m); polytope > $p2=polarize($p1); polytope > $p3=new Polytope(POINTS=>rand_vert($p2->VERTICES,$n)); polytope > print $p3->SIMPLICIAL, " ", $p3->SIMPLE, "\n", $p3->F_VECTOR; 0 0 30 166 264 128

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