The Five-Fold Maps study investigates mapping aperiodic patterns onto three-dimensional forms with icosahedral symmetry. The research explores how two-dimensional quasicrystalline tiling patterns project onto spherical and polyhedral surfaces while maintaining their mathematical properties. Ammann bars and related five-fold decorative systems serve as structural organizing principles that extend beyond surface decoration. These patterns theoretically penetrate inward, dividing volumes into fractal tetrahedral arrangements. The investigation examines how planar aperiodic systems translate to three-dimensional spatial organization. The study tests how five-fold symmetry patterns adapt to curved and polyhedral surfaces. The research addresses how hierarchical subdivision follows aperiodic logic when applied to icosahedral forms, creating connections between two-dimensional quasicrystalline patterns and three-dimensional structural systems.
Photography: Phillip C. Reiner
