Determine whether non-symmetric monotiles outside the reflection-free families admit reflection-free tilings

Determine whether every convex pentagonal monotile without line symmetry belonging only to Type 2 or to Types 7–13 outside Type 1 can generate a tiling without using reflected tiles.

Background

The paper establishes that convex pentagonal monotiles in Types 1 and 3–6 can generate tilings without reflected tiles, whereas the representative tilings for several other families require reflections. It then isolates the remaining non-line-symmetric cases as the Type 2-only monotiles and the Type 7–13 monotiles not contained in Type 1. Whether all of these remaining monotiles admit reflection-free tilings is explicitly left unresolved.