(* Mathematica Graphics3D program for A047762 example.
This program produces a chiral pair (5 cells each) of the tetrahedral clusters with achiral symmetry of type E. 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[p2, p4, p1, p3]; p6 = newp[p2, p3, p1, p4];
p7 = newp[p2, p4, p5, p1]; p8 = newp[p6, p3, p1, p2];
q1 = {3, 0, 0}; q2 = {3, 1, 1}; q3 = {2, 0, 1}; q4 = {2, 1, 0};
q5 = newp[q2, q4, q1, q3]; q6 = newp[q2, q3, q1, q4];
q7 = newp[q2, q4, q5, q1]; q8 = newp[q6, q3, q1, q2];
Show[Graphics3D[{{RGBColor[0, 1, 0], 
    Sphere[{p1, p2, p3, p4, p5, p6, p7, p8, q1, q2, q3, q4, q5, q6, 
      q7, q8}, 0.05]}, {RGBColor[0, 1, 0], 
    Sphere[{p2}, 0.0]}, {RGBColor[1, 0.6, 0.6], 
    Cylinder[{{p1, p2}, {p1, p3}, {p1, p4}, {p2, p3}, {p2, p4}, {p3, 
       p4}, {q5, q1}, {q5, q2}, {q5, q4}, {q6, q1}, {q6, q2}, {q6, 
       q3}, {q7, q2}, {q7, q4}, {q7, q5}, {q8, q1}, {q8, q3}, {q8, 
       q6}}, 0.025]}, {RGBColor[0.6, 0.6, 1], 
    Cylinder[{{q1, q2}, {q1, q3}, {q1, q4}, {q2, q3}, {q2, q4}, {q3, 
       q4}, {p5, p1}, {p5, p2}, {p5, p4}, {p6, p1}, {p6, p2}, {p6, 
       p3}, {p7, p2}, {p7, p4}, {p7, p5}, {p8, p1}, {p8, p3}, {p8, 
       p6}}, 0.025]}}], Boxed -> False, ViewPoint -> {3, 4, 5}]