Artificial intelligent assistant

Combining rhombic dodecahedrons to form a bigger rhombic dodecahedron the classic rhombic dodecahedron (RD) can be used to fill space as shown here I know I cannot recreate a bigger RD by stacking RD together because you never have two touching faces on the sames plane. I am wondering if joining the center of stacked RD you would end up with a bigger RD ? I've tried making origami model and it looks like it is not the case.

If I understand your question correctly it is possible. When you take a grid made up of Rhombic Dodecahedron you can create an RD which has edges four times as long as your unit RDs by joining up the centers of certain RDs in your grid.

The image shows how this works. Five (slightly bluish) RDs have been drawn with their centers on a (pretty random) selection of corners of a larger red RD. Between these corner RDs I have drawn a few connecting RDs to show that they are all correctly drawn in the grid.

Large Rhombic Dodecahedron in a grid of RDs

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