(* Mathematica Graphics3D program for A047775 examples.
This program produces two (5 cells each) of the tetrahedral clusters with achiral symmetry of type B. 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[p3, p4, p1, p2]; p6 = newp[p4, p1, p2, p3];
p7 = newp[p3, p1, p5, p4]; p8 = newp[p1, p2, p6, p4]; q1 = p1 + {-2, 3, 1};
q2 = p2 + {-2, 3, 1}; q3 = p3 + {-2, 3, 1}; q4 = p4 + {-2, 3, 1};
q5 = newp[q3, q4, q1, q2]; q6 = newp[q4, q1, q2, q3];
q7 = newp[q2, q3, q1, q4]; q8 = newp[q2, q3, q7, q1];
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[{q1}, 0.1]}, {RGBColor[1, 0.6, 0.6], 
    Cylinder[{{p1, p2}, {p1, p3}, {p1, p4}, {p2, p3}, {p2, p4}, {p3, 
       p4}, {q1, q2}, {q1, q3}, {q1, q4}, {q2, q3}, {q2, q4}, {q3, 
       q4}}, 0.025]}, {RGBColor[0.6, 0.6, 1], 
    Cylinder[{{p5, p3}, {p5, p4}, {p5, p1}, {p6, p4}, {p6, p1}, {p6, 
       p2}, {p7, p3}, {p7, p1}, {p7, p5}, {p8, p1}, {p8, p2}, {p8, 
       p6}, {q5, q3}, {q5, q4}, {q5, q1}, {q6, q4}, {q6, q1}, {q6, 
       q2}, {q7, q3}, {q7, q1}, {q7, q2}, {q8, q3}, {q8, q7}, {q8, 
       q2}}, 0.025]}}], Boxed -> False, ViewPoint -> {3, 4, 5}]