How can I draw a grid of an fcc lattice?

user_17211043 0
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I have a file with coordinates {x, y,z} of a fcc lattice.

In[0]: data = Import[
  "D:\\AtomsDiffusion\\AtomsDiffusion\\bin\\PositionsAtomsMathematica.\
txt", "CSV"]

Out[0]: {{0, 0, 0}, {0, 0.707, 0.707}, {0.707, 0, 0.707}, {0.707, 0.707, 
  0}, {0, 0, 1.414}, {0, 0.707, 2.121}, {0.707, 0, 2.121}, {0.707, 
  0.707, 1.414}, {0, 1.414, 0}, {0, 2.121, 0.707}, {0.707, 1.414, 
  0.707}, {0.707, 2.121, 0}, {0, 1.414, 1.414}, {0, 2.121, 
  2.121}, {0.707, 1.414, 2.121}, {0.707, 2.121, 1.414}, {1.414, 0, 
  0}, {1.414, 0.707, 0.707}, {2.121, 0, 0.707}, {2.121, 0.707, 
  0}, {1.414, 0, 1.414}, {1.414, 0.707, 2.121}, {2.121, 0, 
  2.121}, {2.121, 0.707, 1.414}, {1.414, 1.414, 0}, {1.414, 2.121, 
  0.707}, {2.121, 1.414, 0.707}, {2.121, 2.121, 0}, {1.414, 1.414, 
  1.414}, {1.414, 2.121, 2.121}, {2.121, 1.414, 2.121}, {2.121, 2.121,
   1.414}};

Using the function Graphics3D, I draw the coordinates:

In[1]: Graphics3D[{Opacity[.6], Ball[#, 0.5] & /@ data}, Axes -> True]

Out:

How can I draw grid lines vertical, horizontal and diagonal,to be like here? example

wolfram-mathematica
1 Answers

Following through on Bill's comment

lines = Catenate@Outer[List[##] &, data, data, 1];

dist = EuclideanDistance @@@ lines;

l2 = First /@ DeleteCases[MapThread[{#1, (#2 > 0 && #2 < 1.5)} &,
     {lines, dist}], {_, False}];

Show[Graphics3D[Line /@ l2, Boxed -> False],
 Graphics3D[{Ball[#, 0.2] & /@ data}, Axes -> True]]

enter image description here

user_8796010
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