Determine whether Type 2–7 intersection monotiles admit non-representative tilings

Determine whether convex pentagonal monotiles in the intersection of the Type 2 and Type 7 families can generate tiling patterns other than the representative tilings of Types 2 and 7, and determine whether any such patterns require reflected tiles.

Background

Convex pentagonal monotiles in the intersection of Types 2 and 7 satisfy additional angle relationships beyond those defining the Type 7 family. They can generate the representative tilings of both Types 2 and 7, and both representative tilings require reflected tiles. The paper explicitly states that it is unresolved whether these same monotiles admit other tiling patterns and, if they do, whether reflections remain necessary.