(* Mathematica Graphics3D program for A047765 examples.
This program produces two (4 and 6 cells) of the tetrahedral clusters with achiral symmetry of type P. The other hexomino has six tetrahedra with a common edge. 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, p3, p4, p1]; p6 = newp[p1, p3, p4, p2]; p7 = newp[p5, p3, p4, p2];
q1 = {5/3, -5/6, -5/6}; q2 = {3, -1/2, -1/2}; q3 = {2, -1/2, 1/2};
q4 = {2, 1/2, -1/2}; q5 = newp[q2, q3, q4, q1]; q6 = newp[q2, q1, q4, q3];
q7 = newp[q2, q5, q4, q3]; q8 = newp[q2, q3, q1, q4]; q9 = newp[q2, q3, q5, q4];
Show[Graphics3D[{{RGBColor[0, 1, 0], 
    Sphere[{p1, p2, p3, p4, p5, p6, p7, q1, q2, q3, q4, q5, q6, q7, 
      q8, q9}, 0.05]}, {RGBColor[0, 1, 0], 
    Sphere[{p5}, 0.0]}, {RGBColor[1, 0.6, 0.6], 
    Cylinder[{{p2, p3}, {p2, p4}, {p3, p4}, {q2, q3}, {q2, q4}, {q3, 
       q4}}, 0.025]}, {RGBColor[0.6, 0.6, 1], 
    Cylinder[{{p1, p2}, {p1, p3}, {p1, p4}, {p5, p2}, {p5, p3}, {p5, 
       p4}, {p6, p1}, {p6, p3}, {p6, p4}, {p7, p5}, {p7, p3}, {p7, 
       p4}, {q1, q2}, {q1, q3}, {q1, q4}, {q5, q2}, {q5, q3}, {q5, 
       q4}, {q6, q2}, {q6, q1}, {q6, q4}, {q7, q2}, {q7, q5}, {q7, 
       q4}, {q8, q2}, {q8, q1}, {q8, q3}, {q9, q2}, {q9, q5}, {q9, 
       q3}}, 0.025]}}], Boxed -> False, ViewPoint -> {-3, -4, 5}]