Convex pentagons and concave octagons that can form rotationally symmetric tilings

TL;DR

This paper explores how convex pentagons can generate rotationally symmetric tilings and how these relate to concave octagons, revealing new geometric properties and pattern formations.

Contribution

It introduces a novel connection between convex pentagons and concave octagons in rotational tilings, expanding understanding of symmetric tiling patterns.

Findings

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

Concave octagons generated by pentagons are equivalent to certain tilings.

Pattern formations include tilings with polygonal holes at the center.

Abstract

In this study, the properties of convex pentagons that can form rotationally symmetric edge-to-edge tilings are discussed. Because the rotationally symmetric tilings are formed by concave octagons that are generated by two convex pentagons connected through a line symmetry, they are considered to be equivalent to rotationally symmetric tilings with concave octagons. In addition, under certain circumstances, tiling-like patterns with a regular polygonal hole at the center can be formed using these convex pentagons.