Non-fundamental trunc-simplex tilings and their optimal hyperball packings and coverings in hyperbolic space I. For families F1-F4

Supergroups of some hyperbolic space groups are classified as a continuation our former works. Fundamental domains will be integer parts truncated tetrahedra belonging to families F1 - F4, for while, by the notation E. Moln?r et al. in 2006. Our paper relies basically on this work. As an application, optimal congruent hyperball packings and coverings truncation base planes with their very good densities computed. This covering density is better than conjecture L. Fejes T?th balls horoballs 1964.