Nonpolygonal growth form of the L‑tetromino substitution tiling

Prove that the growth form of the L‑tetromino substitution tiling (constructed from the standard L‑tetromino via the inflation and dissection rules described in the paper) is not a polygon.

Background

The L‑tetromino tiling is a classical substitution tiling with a single prototile shaped like an L. The authors provide computational evidence suggesting its growth form deviates from polygonal shapes.

They formalize this as a conjecture, seeking a proof that the resulting growth form is nonpolygonal, in contrast to many known periodic and grid cases where growth forms are convex polytopes.