Convex pentagons and convex hexagons that can form rotationally symmetric tilings

TL;DR

This paper investigates the properties of convex hexagons and pentagons capable of forming rotationally symmetric tilings, including edge-to-edge and non-edge-to-edge patterns, and explores tiling-like patterns with polygonal holes.

Contribution

It introduces new classes of convex polygons that can generate rotationally symmetric tilings, expanding understanding of tiling possibilities with convex polygons.

Findings

Convex hexagons can form rotationally symmetric edge-to-edge tilings.

Bisected convex hexagons generate convex pentagons that form non-edge-to-edge tilings.

Tiling-like patterns with polygonal holes can be created using these polygons.

Abstract

In this study, the properties of convex hexagons that can form rotationally symmetric edge-to-edge tilings are discussed. Because the convex hexagons are equilateral convex parallelohexagons, convex pentagons generated by bisecting the hexagons can form rotationally symmetric non-edge-to-edge tilings. In addition, under certain circumstances, tiling-like patterns with an equilateral convex polygonal hole at the center can be formed using these convex hexagons or pentagons.