Research
Cross-cultural studies in sacred geometry
The Platonic Solids — Five Perfect Forms
The five regular convex polyhedra — tetrahedron, cube, octahedron, dodecahedron, icosahedron — their mathematical properties, the *Timaeus* element-attribution, the duality structure, the discovery and reception across Greek, Islamic, Vedic, and African traditions, and the Kepler–Coxeter unfolding into modern geometry.
African Fractal Patterns — Indigenous Computational Geometry
Ron Eglash's research on fractal geometry in African architecture, textiles, divination, cosmology, and social organization — and the broader argument that recursive self-similar geometry is a foundational, intentional principle of Sub-Saharan African design rather than ornamentation.
Islamic Geometric Art — Tessellation, Girih, Muqarnas, and the Quasi-Crystalline Tradition
The Islamic geometric tradition from the 8th to the 16th centuries — symmetry analysis, the girih tile system, muqarnas vaulting, the Darb-i Imam quasi-crystalline pattern that anticipated Penrose tilings by half a millennium, and the mathematical principles underlying Andalusian, Persian, Mughal, and Ottoman geometric design.
The Flower of Life — Cross-Cultural Occurrences of an Overlapping-Circle Pattern
The hexagonal pattern of overlapping circles known as the Flower of Life — its archaeological occurrences (Abydos, Lalibela, China, India), the underlying mathematical structure (vesica piscis, hexagonal close-packing), the modern esoteric reception, and the relationship to legitimate sacred-geometry traditions.