## L-Tetracubes with Pegs and Notches

There are 18*17 = 306 L-Tetracubes with exactly one peg and one notch. The total volume is 1224 and I tried to construct a 4x6x51 box with these pieces but this was rather difficult. Since each piece has a dual one with peg and notch swapped, I decided to construct one half of the box using only one piece of each dual pair. Then the second half is given by swapping the pegs and notches.

Half the construction was divided into a 4x12x6 box, two 2x3x24 boxes and a kind of stair with a bottom area of size 4x6. First the stair was solved and then the large box was filled layer by layer. During this stage pieces inept for the 2x3x24 boxes were preferred. After the first 2x3x24 box was solved leaving no bad pieces, it was also possible to get a solution for the second 2x3x24 box.

There are 18 pieces with exactly one male and 18 pieces with one female face, because the L-Tetracube has 18 square faces and no symmetry. Initally I used this set only to ease a construction together with the 306 pieces with both a peg and a notch. Figures with this set alone are rather easy to get. Shown are two 3x4x6 boxes and two 2x3x12 boxes, which can be combined to get 6x4x6, 3x8x6, 3x4x12, 2x6x12 and 2x3x24 boxes.

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