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
Many years later in 2017 I tried to make real constructions with 3D-printed pieces. With the above computer solutions
I could only finish the six cubes and the truncated roof. One of the four 4x4x6 boxes and the square ring have
pieces, which are wrapped around each other and the real construction failed. Can you find out, where this happend?
New solutions and pictures with the printed pieces are at my
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.