(* Mathematica Graphics3D program for A047766 examples. *)
(* This first program produces one (14 cells) of the tetrahedral clusters with achiral symmetry of type N. The output can be manipulated with the cursor to rotate the figure. *)
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 = newp[p1, p2, p4, p3]; p7 = newp[p1, p2, p3, p4];
p8 = newp[p1, p3, p5, p4]; p9 = newp[p1, p6, p4, p2]; p10 = newp[p1, p2, p7, p3];
q1 = newp[p2, p3, p4, p1];
q5 = newp[q1, p3, p4, p2]; q6 = newp[q1, p2, p4, p3]; q7 = newp[q1, p2, p3, p4];
q8 = newp[q1, p3, q5, p4]; q9 = newp[q1, q6, p4, p2]; q10 = newp[q1, p2, q7, p3];
Show[Graphics3D[{{RGBColor[0, 1, 0], 
    Sphere[{p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, q1, q5, q6, q7, 
      q8, q9, q10}, 0.05]}, {RGBColor[0, 1, 0], 
    Sphere[{p1}, 0.1]}, {RGBColor[1, 0.6, 0.6], 
    Cylinder[{{p2, p3}, {p3, p4}, {p2, p4}}, 0.025]}, {RGBColor[0.6, 
     0.6, 1], 
    Cylinder[{{p1, p2}, {p1, p3}, {p1, p4}, {p5, p1}, {p5, p3}, {p5, 
       p4}, {p6, p1}, {p6, p2}, {p6, p4}, {p7, p1}, {p7, p2}, {p7, 
       p3}, {p8, p1}, {p8, p5}, {p8, p3}, {p9, p1}, {p9, p4}, {p9, 
       p6}, {p10, p1}, {p10, p2}, {p10, p7}, {q1, p2}, {q1, p3}, {q1, 
       p4}, {q5, q1}, {q5, p3}, {q5, p4}, {q6, q1}, {q6, p2}, {q6, 
       p4}, {q7, q1}, {q7, p2}, {q7, p3}, {q8, q1}, {q8, q5}, {q8, 
       p3}, {q9, q1}, {q9, p4}, {q9, q6}, {q10, q1}, {q10, p2}, {q10, 
       q7}}, 0.025]}}], Boxed -> False, ViewPoint -> {3, -4, 5}]

(* This second program produces a chiral pair (14 cells each) of the tetrahedral clusters with chiral symmetry of type O. The output can be manipulated with the cursor to rotate the figure. *)
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 = newp[p1, p2, p4, p3]; p7 = newp[p1, p2, p3, p4];
p8 = newp[p1, p3, p5, p4]; p9 = newp[p1, p6, p4, p2]; p10 = newp[p1, p2, p7, p3];
q1 = newp[p2, p3, p4, p1];
q5 = newp[q1, p3, p4, p2]; q6 = newp[q1, p2, p4, p3]; q7 = newp[q1, p2, p3, p4];
q8 = newp[q1, p4, q5, p3]; q9 = newp[q1, q6, p2, p4]; q10 = newp[q1, p3, q7, p2];
adj = {3, -3, 0};
r1 = p1 + adj; r2 = p3 + adj; r3 = p2 + adj; r4 = p4 + adj;
r5 = newp[r1, r3, r4, r2]; r6 = newp[r1, r2, r4, r3]; r7 = newp[r1, r2, r3, r4];
r8 = newp[r1, r3, r5, r4]; r9 = newp[r1, r6, r4, r2]; r10 = newp[r1, r2, r7, r3];
s1 = newp[r2, r3, r4, r1];
s5 = newp[s1, r3, r4, r2]; s6 = newp[s1, r2, r4, r3]; s7 = newp[s1, r2, r3, r4];
s8 = newp[s1, r4, s5, r3]; s9 = newp[s1, s6, r2, r4]; s10 = 
 newp[s1, r3, s7, r2];
Show[Graphics3D[{{RGBColor[0, 1, 0], 
    Sphere[{p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, q1, q5, q6, q7, 
      q8, q9, q10, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, s1, s5, 
      s6, s7, s8, s9, s10}, 0.05]}, {RGBColor[0, 1, 0], 
    Sphere[{p1}, 0.0]}, {RGBColor[1, 0.6, 0.6], 
    Cylinder[{{p2, p3}, {p3, p4}, {p2, p4}, {r1, r2}, {r1, r3}, {r1, 
       r4}, {r5, r1}, {r5, r3}, {r5, r4}, {r6, r1}, {r6, r2}, {r6, 
       r4}, {r7, r1}, {r7, r2}, {r7, r3}, {r8, r1}, {r8, r5}, {r8, 
       r3}, {r9, r1}, {r9, r4}, {r9, r6}, {r10, r1}, {r10, r2}, {r10, 
       r7}, {s1, r2}, {s1, r3}, {s1, r4}, {s5, s1}, {s5, r3}, {s5, 
       r4}, {s6, s1}, {s6, r2}, {s6, r4}, {s7, s1}, {s7, r2}, {s7, 
       r3}, {s8, s1}, {s8, s5}, {s8, r4}, {s9, s1}, {s9, r2}, {s9, 
       s6}, {s10, s1}, {s10, r3}, {s10, s7}}, 0.025]}, {RGBColor[0.6, 
     0.6, 1], 
    Cylinder[{{p1, p2}, {p1, p3}, {p1, p4}, {p5, p1}, {p5, p3}, {p5, 
       p4}, {p6, p1}, {p6, p2}, {p6, p4}, {p7, p1}, {p7, p2}, {p7, 
       p3}, {p8, p1}, {p8, p5}, {p8, p3}, {p9, p1}, {p9, p4}, {p9, 
       p6}, {p10, p1}, {p10, p2}, {p10, p7}, {q1, p2}, {q1, p3}, {q1, 
       p4}, {q5, q1}, {q5, p3}, {q5, p4}, {q6, q1}, {q6, p2}, {q6, 
       p4}, {q7, q1}, {q7, p2}, {q7, p3}, {q8, q1}, {q8, q5}, {q8, 
       p4}, {q9, q1}, {q9, p2}, {q9, q6}, {q10, q1}, {q10, p3}, {q10, 
       q7}, {r2, r3}, {r3, r4}, {r2, r4}}, 0.025]}}], Boxed -> False, 
 ViewPoint -> {3, 4, -5}]