There are only a few polyhedra which can fill space without leaving gaps, without “help” from a second polyhedron. This filling of space is the three-dimensional version of tessellating a plane. Among those that can do this are the cube, the truncated octahedron, and the rhombic dodecahedron.
If multiple polyhedra are allowed in a space-filling pattern, this opens new possibilities. Here is one: the filling of space by cuboctahedra and octahedra. There are others, and they are likely to appear as future blog-posts here.
Software credit: I made this virtual model using Stella 4d, polyhedral-manipulation software you can buy, or try as a free trial download, at http://www.software3d.com/Stella.php.
RobertLovesPi.net 
This is a rectified cubic honeycomb, r{4,3,4}. New vertices are inserted mid-edge to the cubic honeycomb. Cubic cells are cut down to cuboctahedra and new octahedral cells are added where the original vertices were.
https://en.wikipedia.org/wiki/Rectified_cubic_honeycomb
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hi,
i was wondering if you would share this wonderful honeycomb Stella file. i really like to investigate it on my Stella software. i need it for my research.
Thanks and great website.
All the best
Talal
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Unfortunately, I didn’t save a .stel file for this construction.
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