Space-filling building blocks of diverse shape permeate nature at all levels of organization, from atoms to honeycombs, and have proven useful in artificial systems, from molecular containers to clay bricks. But, despite the wide variety of space-filling polyhedra known to mathematics, only the cube has been explored in robotics. Thus, here we roboticize a non-cubic space-filling shape: the rhombic dodecahedron. This geometry offers an appealing alternative to cubes as it greatly simplifies rotational motion of one cell about the edge of another, and increases the number of neighbors each cell can communicate with and hold on to. To better understand the challenges and opportunities of these and other space-filling machines, we manufactured 48 rhombic dodecahedral cells and used them to build various superstructures. We report locomotive ability of some of the structures we built, and discuss the dis/advantages of the different designs we tested. We also introduce a strategy for genderless passive docking of cells that generalizes to any polyhedra with radially symmetrical faces. Future work will allow the cells to freely roll/rotate about one another so that they may realize the full potential of their unique shape.