Converting tilings with multiple types of rhombuses to pentagonal tilings

2022/03/09 by Teruhisa Sugimoto, Sugimoto, Teruhisa
Materials Science · Engineering · #Quasicrystal Structures and Properties #graph theory and CDMA systems #Advanced Materials and Mechanics

paper · pdf · doi:10.48550/arxiv.2203.04457

Abstract

The results involving rotationally symmetric tilings with multiple types of rhombuses, discovered by Penrose, Ammann, Beenker, or Socolar, are converted to tilings with multiple types of pentagons are presented. The pentagons can be convex or concave, and can be degenerated into a trapezoid or parallelogram. If the pentagons are convex, they belong to the Type 2 family.

Related

• Pentagons and rhombuses that can form rotationally symmetric tilings
• Convex pentagons and concave octagons that can form rotationally symmetric tilings
• Rotationally Symmetric Tilings with Convex Pentagons and Hexagons
• Rotationally symmetric tilings with convex pentagons belonging to both the Type 1 and Type 7 families
• Convex Pentagon Tilings and Heptiamonds, II