If, instead of diamonds, we join triamonds (trapezia) together then we get subsets of the 3n-iamonds which we can call polytraps. There are 9 ditraps shown in a number of constructions below. The 15 piece one-sided set can also make a number of figures.

The following table is due to Brendan Owen.

The 94 tritraps include one piece with a hole. The 93 pieces without a hole can form a trapezium as shown below.

Beolw are two constructions, one with the full set and the other without the piece with a hole.

The full set can be used to make 11-fold copies of an heptiamond with a hole.

The 178 one-sided tritraps without a hole are shown here.

Constructions with the chequered sets are also possible.