(* Mathematica Graphics3D program for A047764 examples.
This program produces two examples (2 and 8 cells) of the tetrahedral clusters with 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 = newp[p1, p3, p4, p2];
p6 = p1 + {-2, 2, 0}; p7 = p2 + {-2, 2, 0}; p8 = p3 + {-2, 2, 0}; p9 = p4 + {-2, 2, 0};
p10 = p5 + {-2, 2, 0};
p11 = newp[p6, p7, p8, p9];
p12 = newp[p6, p7, p9, p8];
p13 = newp[p8, p7, p9, p6];
p14 = newp[p6, p10, p8, p9];
p15 = newp[p6, p10, p9, p8];
p16 = newp[p8, p10, p9, p6];
Show[Graphics3D[{{RGBColor[0, 1, 0], 
    Sphere[{p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, p11, p12, p13, 
      p14, p15, p16}, 0.05]}, {RGBColor[0, 1, 0], 
    Sphere[{p1, p3, p4}, 0.0]}, {RGBColor[1, 0.6, 0.6], 
    Cylinder[{{p1, p3}, {p1, p4}, {p3, p4}, {p6, p8}, {p6, p9}, {p8, 
       p9}}, 0.025]}, {RGBColor[0.6, 0.6, 1], 
    Cylinder[{{p1, p2}, {p2, p3}, {p2, p4}, {p5, p1}, {p5, p3}, {p5, 
       p4}, {p6, p7}, {p7, p8}, {p7, p9}, {p10, p6}, {p10, p8}, {p10, 
       p9}, {p6, p11}, {p7, p11}, {p8, p11}, {p6, p12}, {p7, 
       p12}, {p9, p12}, {p8, p13}, {p7, p13}, {p9, p13}, {p6, 
       p14}, {p10, p14}, {p8, p14}, {p6, p15}, {p10, p15}, {p9, 
       p15}, {p8, p16}, {p10, p16}, {p9, p16}}, 0.025]}}], 
 Boxed -> False, ViewPoint -> {3, 4, 5}]