(* Mathematica Graphics3D program for A047774 examples.
This program produces two chiral pairs (7 and 8 cells each) of the tetrahedral clusters with chiral symmetry of type C. 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];
q0 = {1, 1, 1}; q2 = {1, 2, 2}; q3 = {2, 1, 2}; q4 = {2, 2, 1};
q1 = newp[q2, q3, q4, q0];
q5 = newp[q1, q3, q4, q2]; q6 = newp[q1, q2, q4, q3]; q7 = newp[q1, q2, q3, q4];
q8 = newp[q1, q3, q5, q4]; q9 = newp[q1, q6, q4, q2]; q10 = newp[q1, q2, q7, q3];
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 = q1 + adj; s2 = q3 + adj; s3 = q2 + adj; s4 = q4 + adj;
s0 = newp[s2, s3, s4, s1];
s5 = newp[s1, s3, s4, s2]; s6 = newp[s1, s2, s4, s3]; s7 = newp[s1, s2, s3, s4];
s8 = newp[s1, s3, s5, s4]; s9 = newp[s1, s6, s4, s2]; s10 = newp[s1, s2, s7, s3];
Show[Graphics3D[{{RGBColor[0, 1, 0], 
    Sphere[{p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, q0, q1, q2, q3, 
      q4, q5, q6, q7, q8, q9, q10, r1, r2, r3, r4, r5, r6, r7, r8, r9,
       r10, s0, s1, s2, s3, s4}, 0.05]}, {RGBColor[0, 1, 0], 
    Sphere[{p2, s3, s0}, 0.0]}, {RGBColor[1, 0.6, 0.6], 
    Cylinder[{{q0, q2}, {q0, q3}, {q0, q4}, {q1, q2}, {q1, q3}, {q1, 
       q4}, {q2, q3}, {q3, q4}, {q2, q4}, {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}, {s5, s1}, {s5, s3}, {s5, 
       s4}, {s6, s1}, {s6, s2}, {s6, s4}, {s7, s1}, {s7, s2}, {s7, 
       s3}, {s8, s1}, {s8, s5}, {s8, s3}, {s9, s1}, {s9, s4}, {s9, 
       s6}, {s10, s1}, {s10, s2}, {s10, s7}, {r1, r2}, {r1, r3}, {r1, 
       r4}, {r2, r3}, {r3, r4}, {r2, r4}}, 0.025]}, {RGBColor[0.6, 
     0.6, 1], 
    Cylinder[{{p1, p2}, {p1, p3}, {p1, p4}, {p2, p3}, {p3, p4}, {p2, 
       p4}, {q5, q1}, {q5, q3}, {q5, q4}, {q6, q1}, {q6, q2}, {q6, 
       q4}, {q7, q1}, {q7, q2}, {q7, q3}, {q8, q1}, {q8, q5}, {q8, 
       q3}, {q9, q1}, {q9, q4}, {q9, q6}, {q10, q1}, {q10, q2}, {q10, 
       q7}, {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}, {s0, s2}, {s0, s3}, {s0, s4}, {s1, s2}, {s1, s3}, {s1, 
       s4}, {s2, s3}, {s3, s4}, {s2, s4}}, 0.025]}}], Boxed -> False, 
 ViewPoint -> {3, -4, 5}]