Rotationally symmetric tilings with convex pentagons belonging to both the Type 1 and Type 7 families

TL;DR

This paper introduces new rotationally symmetric tilings using convex pentagons that belong to both Type 1 and Type 7 families, featuring spiral patterns with specific symmetries and edge-to-edge connections.

Contribution

It presents the first known rotationally symmetric tilings with convex pentagons that simultaneously belong to both Type 1 and Type 7 families, including spiral tilings with unique symmetry properties.

Findings

Tilings are edge-to-edge and have no reflection symmetry.

Includes spiral tilings with two- and four-fold rotational symmetry.

Connects pentagon families to new symmetric tiling patterns.

Abstract

Rotationally symmetric tilings by a convex pentagonal tile belonging to both the Type 1 and Type 7 families are introduced. Among them are spiral tilings with two- and four-fold rotational symmetry. Those rotationally symmetric tilings are connected edge-to-edge and have no axis of reflection symmetry.