Dear Atome;
Why not additionally think about:
1.57 *10-8 cm = 1.57 * 10-10 m = 157 pm
All other numeric I did not test, as other have done it.
Good Luck!
ARGOS++
Dear Atome;
And if you correct your calculations by the factor for “Regular Sphere Packing”:
157 pm * (0.74048)1/3 = 157 pm * 0.9047 = 142.05 pm
I think that’s pretty close for the precision you were taking.
For “Regular Sphere Packing” see under: "Sphere Packing (http://en.wikipedia.org/wiki/Sphere_packing)”
I hope it may be of help to you.
Good Luck!
ARGOS++