What Platonic or other solid shapes tesselate to fill space or fill space with only cubes between them?

Question

I am trying to determine which geometric solids might best be used in an experimental housing design. I would like the shapes to be able to join together and completely fill space, yet have workable flooring, or almost fill space with cubes left between.

Answer 1

only cubes would leave cubeshaped spaces. pyramids would leave pyramidial shapes, so on so forth.... try cubes or dodecahedrons.