Exhaustive search of convex pentagons which tile the plane

TL;DR

This paper exhaustively searches for all convex pentagons that can tile the plane, confirming that only the 15 known families exist and that no convex polygon can produce only non-periodic tilings.

Contribution

It provides a comprehensive verification that no additional convex pentagon families exist beyond the known 15, and proves the absence of convex polygons that tile only non-periodically.

Findings

Confirmed the 15 known convex pentagon tiling families.

Proved no convex polygon can tile exclusively non-periodically.

Established the completeness of convex pentagon tiling classifications.

Abstract

We present an exhaustive search of all families of convex pentagons which tile the plane. This research shows that there are no more than the already 15 known families. In particular, this implies that there is no convex polygon which allows only non-periodic tilings.