  We introduce a family of 3D combinatorial objects that we define as minimal
3D polyominoes inscribed in a rectanglar prism. These objects are connected
sets of unitary cubic cells inscribed in a given rectangular prism and of
minimal volume under this condition. They extend the concept of 2D polyominoes
inscribed in a rectangle defined in a previous work. Using their geometric
structure and elementary combinatorial arguments, we construct generating
functions of minimal 3D polyominoes in the form of rational functions. We also
obtain a number of exact formulas and recurrences for sub-families of these
polyominoes.
