We have six different pieces, two straight ones, three pieces with different angles and a triangle. Look at the positions of connected squares and the positions of connected hexagons to take and orientate the right piece for a given structure. I built the following figures.

Some more constructions are suggested at Marc Owen's site.

Among the six pieces there are five pieces that fit a hexagonal grid and a triangle of size 5 can be made.

If we add the smaller trocs of order 1 or 2 we have nine polytrocs with a total volume of 23 units. I printed a box, which can be packed with the pieces. obj-files for the pieces and the box are available at thingiverse

Some symmetric figures are shown.

Only one piece doesn't fit the hexagonal grid. The remaining pieces have a total volume of 20 and can be used for a 4x5 parallelogram.

Stewart T.Coffin suggested a puzzle with the four non-straight tritrocs and the ditroc with a square connection. A nice little cuboid and a pyramid can be made.

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