I have no idea what the "binary icosahedron" should be; and so there is no standard polymake function for this. Please explain.
As far as saving files from a visualization is concerned, please consult our tutorial.
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polytope > @list_of_cones = (); for (my $i=0; $i<5; ++$i) { my $C = new Cone(INPUT_RAYS=>[[1,0],[1,$i]]); push @list_of_cones, $C; }
polytope > $u = fan::union_of_cones(\@list_of_cones);
polytope > print $u->F_VECTOR;
5 4
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$quadric = toTropicalPolynomial("max(2*x,w+x+y,2*w+2*y,w+y+z,2*z,4*w)");