construct a lattice with a defined unitcell

Question

We can construct a base-centered tetragonal unit cell by:

LatticeData["CenteredTetragonal", "Image"]

But how can we construct a lattice by 8 of this unit cell (put them together)? For example, 4 unit cells on the top and 4 unit cells on the bottom of the lattice.

Here there is a trick for simple cubic but it does not work for may lattice!

Answer 1

ClearAll[latticeGrid]
latticeGrid[{lattice_String, {x_, y_, z_}}, opts : OptionsPattern[]] := 
 Module[{ld = LatticeData[lattice, "Image"], lengths, 
      tuples = Tuples[Range[0, # - 1] & /@ {x, y, z}]}, 
  lengths = -Subtract @@@ CoordinateBounds @ 
      DiscretizeGraphics[ld /. ( Sphere[__]:> {})];
  Show[ld /. prim : (_Polygon | _Line | _Sphere) :> 
      Translate[prim, lengths # & /@ tuples], opts]]

Examples:

latticeGrid[{"CenteredTetragonal", {4, 1, 2}}, ViewPoint -> {1, -3, 1}]

latticeGrid[{"CenteredTetragonal", {2, 2, 3}}, ViewPoint -> {1, -3, 1}]

latticeGrid[{"FaceCenteredCubic", {3, 1, 3}}, ViewPoint -> {1, -3, 1}]

latticeGrid[{"TetrahedralPacking", {3, 1, 2}}, ViewPoint -> {1, -3, 1}]