  Flat-band models have been of particular interest from both fundamental
aspects and realization in materials. Beyond the canonical examples such as
Lieb lattices and line graphs, a variety of tight-binding models are found to
possess flat bands. However, analytical treatment of dispersion relations is
limited, especially when there are multiple flat bands with different energies.
In this paper, we present how to determine flat-band energies and wave
functions in tight-binding models on decorated diamond and pyrochlore lattices
in generic dimensions $D \geq 2$. For two and three dimensions, such lattice
structures are relevant to various organic and inorganic materials, and thus
our method will be useful to analyze the band structures of these materials.
