(* Mathematica Graphics3D program for A047753 example. This program produces one (9 cells) of the tetrahedral clusters with achiral symmetry of type I. The output can be manipulated with the cursor to rotate the figure. *) newp[a_, b_, c_, d_ ] := 2 (a + b + c)/3 - d; p1 = {0, 0, 0}; p2 = {0, 1, 1}; p3 = {1, 0, 1}; p4 = {1, 1, 0}; p5 = newp[p1, p2, p3, p4]; p6 = newp[p2, p3, p4, p1]; p7 = newp[p3, p4, p1, p2]; p8 = newp[p4, p1, p2, p3]; p9 = newp[p5, p1, p2, p3]; p10 = newp[p8, p1, p2, p4]; p11 = newp[p3, p4, p7, p1]; p12 = newp[p3, p4, p6, p2]; Show[Graphics3D[{{RGBColor[0, 1, 0], Sphere[{p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, p11, p12}, 0.05]}, {RGBColor[1, 0.6, 0.6], Cylinder[{{p1, p2}, {p1, p3}, {p1, p4}, {p2, p3}, {p2, p4}, {p3, p4}}, 0.025]}, {RGBColor[0, 1, 0], Sphere[{p2}, 0.0]}, {RGBColor[0.6, 0.6, 1], Cylinder[{{p1, p5}, {p2, p5}, {p3, p5}, {p2, p6}, {p3, p6}, {p4, p6}, {p3, p7}, {p4, p7}, {p1, p7}, {p4, p8}, {p1, p8}, {p2, p8}, {p1, p9}, {p2, p9}, {p5, p9}, {p1, p10}, {p2, p10}, {p8, p10}, {p3, p11}, {p4, p11}, {p7, p11}, {p3, p12}, {p4, p12}, {p6, p12}}, 0.025]}}], Boxed -> False, ViewPoint -> {3, 4, 5}]