Pseudo-Polycubes with up to 4 Cubes
There are 100 pseudo-polycubes with 4 or less cubes. The nasty parity problem with the
pseudo-tetracubes disappears and the total volume of 384 = 4*4*4*6 allows für multiple
constructions as seen below.
Here are the solutions for
the 4 boxes,
the 6 cubes,
the ring and
The 30 flat pseudo-polycubes with order 4 or less have a total volume of 108 = 2*2*3*3*3. Some solid and open boxes are shown.
The layers for the constructions are here .
The 6x6x3 box is a 3-fold replica of the square tetromino. For three other solid tetrominoes a 3-fold replica is also
possible. But we cannot replicate the I-Tetromino because piece no 15 doesn't fit into a 3x3x12 box. For the numbering
look at the picture of the pieces.