Pentagons and rhombuses that can form rotationally symmetric tilings

TL;DR

This paper explores how convex and concave pentagons related to rhombuses can form various rotationally symmetric tilings, highlighting their geometric properties and correspondence with rhombic tilings.

Contribution

It introduces a classification of pentagons based on their relation to rhombuses and discusses their role in creating symmetric tilings.

Findings

Convex pentagons belong to the Type 2 family.

Pentagons can degenerate into trapezoids.

Correspondence between pentagons and rhombic tilings is established.

Abstract

In this study, various rotationally symmetric tilings that can be formed using pentagons that are related to rhombus are discussed. The pentagons can be convex or concave and can be degenerated into a trapezoid. If the pentagons are convex, they belong to the Type 2 family. Because the properties of pentagons correspond to those of rhombuses, the study also explains the correspondence between pentagons and various rhombic tilings.