GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
18 Hilbert basis elements of degree 1 4 extreme rays 4 support hyperplanes embedding dimension = 4 rank = 4 (maximal) external index = 1 internal index = 30 grading: 0 0 0 1 degrees of extreme rays: 1: 4 *********************************************************************** 18 Hilbert basis elements of degree 1: 0 0 0 1 0 0 1 1 0 0 2 1 0 0 3 1 0 0 4 1 0 0 5 1 0 1 0 1 0 1 1 1 0 1 2 1 0 1 3 1 0 2 0 1 0 2 1 1 0 3 0 1 1 0 0 1 1 0 1 1 1 0 2 1 1 1 0 1 2 0 0 1 4 extreme rays: 0 0 0 1 0 0 5 1 0 3 0 1 2 0 0 1 4 support hyperplanes: -15 -10 -6 30 0 0 1 0 0 1 0 0 1 0 0 0