Solid 4.5-ominoes

Take the solid tetrominoes and add a sliced cube, so that one or two vertical square faces are touching. The triangular faces of the sliced cube may be vertical or horizontal. Together we have 72 pieces with a total volume of 72*4.5=324 unit cubes. Since 324 factorizes very well it's possible to construct multiple rectangles, boxes and some other figures.