(* Mathematica Graphics3D program for A047751 examples. This program produces two examples (1 and 5 cells) of the tetrahedral clusters with maximal symmetry (type K). The output can be manipulated with the cursor to rotate the figures. *) 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 = p1 + {-2, 2, 0}; p6 = p2 + {-2, 2, 0}; p7 = p3 + {-2, 2, 0}; p8 = p4 + {-2, 2, 0}; p9 = newp[p5, p6, p7, p8]; p10 = newp[p6, p7, p8, p5]; p11 = newp[p7, p8, p5, p6]; p12 = newp[p8, p5, p6, p7]; 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}, {p5, p6}, {p5, p7}, {p5, p8}, {p6, p7}, {p6, p8}, {p7, p8}}, 0.025]}, {RGBColor[0.6, 0.6, 1], Cylinder[{{p5, p9}, {p6, p9}, {p7, p9}, {p6, p10}, {p7, p10}, {p8, p10}, {p7, p11}, {p8, p11}, {p5, p11}, {p6, p12}, {p8, p12}, {p5, p12}}, 0.025]}}], Boxed -> False, ViewPoint -> {3, 4, 5}]