Four kites form a single Tetrakite that fits into the grid shown.

Note:
The grid used here is composed of offset kites and does not have an established name. For this reason, the term Tetrakites is used for this puzzle, in order to distinguish it from the Honeycomb Tetrakites, which are based on a regular hexagonal honeycomb grid.

There are several Polykites that fit into this grid:

2 Dikites, 4 Trikites, 13 Tetrakites, 34 Pentakites, and 120 Hexakites.

The 13 Tetrakites cover an area of 52 kites.

The underlying kite grid has no global mirror axes; its only non-trivial symmetry is a 180° rotational symmetry. Global reflection axes are entirely absent. However, local mirror axes do exist (for example, along the long diagonals of the individual kites), which means that on this grid it is possible to construct shapes that exhibit either 180° rotational symmetry or reflective symmetry.

The shapes shown here make use of these local mirror axes and each has a single axis of reflection.

All pieces, shapes, and solutions were generated using the program PolySolver.

The 3D-print templates consist of the 13 Tetrakite puzzle pieces and a box.