Just because a polyhedron can tile 3D space, doesn't mean you should try to turn it into a Lego piece. This is a technical print and the final pieces are ridiculous to build with. Printing this is bound to be a frustrating waste of your time. Don't say I didn't warn you :)
If you have some time and energy to waste, print two of the "Parallelepiped (half)" and one of the "Connector" files for each piece. The connector piece fits between the two halves to ensure that the faces line up. Print without a brim if possible to minimize extra material getting in the way. As with any construction objects, print as high quality as possible and expect to do a bit of post-print finishing for a perfect fit.
The above models were printed with a 0.4 mm nozzle at 0.1 mm layer height.
The parallelepiped is essentially an octahedron with two tetrahedrons attached to opposite faces, so the tiling is base on the octahedron and tetrahedron pattern found in an isotropic vector matrix.
On a technical note, the hole and nub are offset .1 mm form the center point of the triangles to compensate for the small but unavoidable gap between two attached pieces. The holes and nubs actually have a negative tolerance to account for the small amount of distortion that results from printing the nubs on an angle.
