This image above has only one polyhedron-type hidden from view, in the center: a red truncated cube. Next, more of this pattern I just found will be added.
The next step will be to add another layer of blue octagonal prisms.
And now, more yellow cubes.
This was an accidental discovery I made, just messing around with Stella 4d, a program you may try for yourself at http://www.software3d.com/Stella.php. The next cells added will be red truncated cubes.
Next up, I’ll add a set of pink rhombcuboctahedra.
The next set of polyhedra added: some yellow cubes, and blue octagonal prisms.
Now I’ll add more of the red truncated cubes.
At this point, more yellow cubes are needed.
The next polyhedra added will be pink rhombcuboctahedra.
And now, more of the blue octagonal prisms.
As long as this pattern is followed, this may be continued without limit, filling space, without leaving any gaps.