  We study minimal-doubling fermion actions on hyperdiamond and deformed
hyperdiamond lattices, with emphasis on the real-space construction of them and
Lorentz covariance of excitations from fermion poles. We propose the improved
spatial construction of Creutz fermion action on a deformed hyperdiamond
lattice, and discuss conditions for a hyperdiamond-lattice action to produce
Lorentz-covariant excitations from poles of fermion propagators. It is pointed
out that the non-nearest-site hoppings are essential for the correct
excitations. We propose a class of minimal-doubling actions defined on a
deformed hypercubic lattice as a generalization of Creutz-type actions. In
addition we introduce a two-parameter class of Wilczek-type minimal-doubling
actions.
