3D Aperiodic Girih Tiles

Year: 2020 Authors: Sam Moradzadeh; Ahad Nejad Ebrahimi

Core claim

Golden-rhombus-based Penrose tilings and PIC-derived girih construction can be extended into 3D aperiodic forms, producing self-supporting girih structures with broad pattern variations.

Topics

Islamic geometric patterns, aperiodic tiling, 3D Penrose tiling, girih tessellation, quasicrystalline symmetry, architectural pattern generation

Domains

tiling theory, symmetry, projections from higher-dimensional lattices, Penrose P2 and P3 prototiles, golden ratio geometry, stellations, Islamic art, architectural ornament

Methods

historical method, polygons in contact (PIC), orthogonal projection, vertex indexing, lattice projection tiling, geometric transformation

Media

golden rhombus, kite and dart prototiles, thick and thin rhombi, decagon-based girih tiles, rhombic hexecontahedron (RH), 3D pattern models

Source status

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