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EXTRA: lat_grid - lattices and grids with integer coordinates

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Usage: lat_grid [options] [lat_type [outer_width [inner_width]]]

Make a lattice or grid with integer coordinates. Lattice types (default: sc)
are followed by name and then and valid strut arguments (squares of length,
first is square of the radius of balls packed at the vertex positions)
  sc                 - Simple Cubic                         (1, 2, 3)
  fcc                - Face Centred Cubic                   (2, 4, 6, 12)
  bcc                - Body Centred Cubic                   (3, 4, 8)
  hcp                - Hexagonal Close Packing              (18)
  rh_dodec           - Rhombic Dodecahedra                  (3, 8)  cubo_oct           - Cuboctahedron / Octahedron           (2)
  tr_oct             - Truncated Octahedron                 (2)
  tr_tet_tet         - Truncated Tetrahedron / Tetrahedron  (2)
  tr_tet_tr_oct_cubo - Truncated Tetrahedron / 
                       Truncated Octahedron / Cuboctahedron (4)
  diamond            - Diamond                              (3)
  hcp_diamond        - HCP Diamond                          (27)
  k_4                - K_4 Crystal                          (2)

Inner and outer widths are the sizes of the inner and outer containers.
For cubes, these are the length of a side, for spheres these are the
squares of the radii.

  -h,--help this help message (run 'off_util -H help' for general help)
  --version version information
  -C <cent> centre of lattice, in form \"x_val,y_val,z_val\"
  -c <type> container, c - cube (default), s - sphere
  -s <len2> create struts, the value is the square of the strut length
  -o <file> write output to file (default: write to standard output)


View a cubic section of Close Cubic Packing
lat_grid fcc 6 | antiview -v b

Make a spherical section of a diamond grid
lat_grid -c s -s 3 diamond 16 | antiview


Spherical container suggested by Steve Waterman, who has made a collection of hulls of spherically contained lattices.

The grids of shortest strut length represent the edges of a packing of polyhedra, with the exception of diamond, HCP diamond and K_4.

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Contact:      -      Modified 27.5.2023