Ammann Grid and Knot Structure of a Quasiperiodic Girih Pattern
Uli Gaenshirt

Proceedings of Bridges 2024: Mathematics, Art, Music, Architecture, Culture
Pages 155–162
Regular Papers

Abstract

Girih patterns have been documented in the Orient since the early Middle Ages. They were generally constructed using geometric stencils. After discussing the quasiperiodic Penrose tilings from the 1970s and the corresponding covering models since the 1990s, appropriate Girih stencils were incorporated into a Penrose rhombus tiling. Subsequently, the resulting quasiperiodic Girih pattern was inserted into an Ammann grid-based covering cell. A very close agreement was found. Furthermore, it is shown that the Girih pattern is interwoven from closed knots of three different types, each of which has a one-to-one relationship with a single tile of the quasiperiodic HBS tiling. The Girih knots are discussed from different angles and illustrated in detail.

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