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I made a single lattice around a cube in the following way:

  1. Added a cube on scene.
  2. In Edit mode I added loopcut with Ctrl+R.
  3. Removed corner vertices.
  4. Converted the cube to curve.
  5. In Object Data tab I changed geometry properties and received next object:

Single lattice

Now I need to make double lattice like this(left side):

Double lattice

But when I made double lattice by previous way I have got object shown in the right side of previous picture.
How can I get a required object?
May be exists better way to make this objects?

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You can either use the wireframe modifier or the skin modifier:

For Wireframe modifier:

  • Add Cube
  • Subdivide with 2 divisions
  • delete edge vertices
  • add wireframe modifier

For skin modifier:

  • Add Cube
  • Subdivide with 2 divisions
  • delete edge vertices
  • delete all faces (faces only!)
  • apply skin modifier
  • Scale with ctrla
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