Determine whether AH-tile and BT-tile admit tilings other than the Tile(1,1)-derived non-periodic tiling

Determine whether the tile set consisting of the two concave polygons AH-tile and BT-tile admits tilings other than the non-periodic tiling \(\mathscr{T}_s\).

Background

The pair AH-tile and BT-tile is known to generate Ts\mathscr{T}_s, whose construction is related to the substitution tiling by Tile(1,1). The paper leaves open whether this pair generates other tilings.

References

A tile set consisting of two types of concave polygons, AH-tile and BT-tile, is known to generate $\mathscr{T}_s$, but whether it admits other tilings remains unknown.

— Tile sets consisting of two types of concave polygons derived from periodic tilings corresponding to non-periodic tilings with hat and turtle tiles  (2609.09603 - Sugimoto, 9 Sep 2026) in Section 5.3, Properties of tile sets containing AH-tile, BH-tile, AT-tile, and BT-tile