A primary parallelohedron is a polyhedron that can fill space with infinite translated copies. It is known (e.g., Coxeter, H. S. M. Regular Polytopes, 3rd ed. New York: Dover, pp. 29-30, 1973; or, Tutton, A. E. H. Crystallography and Practical Crystal Measurement, 2nd ed. London: Lubrecht & Cramer, 1964.) that the primary parallelohedra are the cube, hexagonal prism, elongated dodecahedron, rhombic dodecahedron, and truncated octahedron. Is there is a classification for any higher dimensions? What are the primary d-parallelotopes? The following is a conjecture of mine regarding the case of $d=4$. ---------- Conjecture: There are exactly 7 primary 4-parallelotopes: (1) Hypercube (2) 16-cell (3) 24-cell (4) Hexagonal Square Duoprism (5) Prismatic Elongated Dodecahedron (6) Prismatic Rhombic Dodecahedron (7) Prismatic Truncated Octahedron