Here is another shape I made up from eight polycairos dubbed the boar.
This new shape can be completely surrounded by 5, 6 or 7 copies of itself.
Central cores of four boars, can be constructed in two ways (light and dark grey). The resulting patterns can be both periodic or aperiodic. Coronas that fully surround the cores, overlap.
Both core types can be surrounded by all eight rotations and mirrors. Unlike the previous examples, the boars that make up the coronas, are not shared.
Boars can produce chains or strips of alternating rotations or mirrors. These can in turn, join adjacently to themselves or other combinations.
In the second of the two patterns below, there are diagonal rows of boars, left to right, which use all four rotations and their mirrors (two different sequences), running either side of two hidden cores.
A few more examples to finish…
Software used… Polyform Puzzle Solver by Jaap Scherphuis https://www.jaapsch.net/puzzles/polysolver.htm and a very old version of Jasc Paintshop Pro 7.0.