The Rhombic Structures study investigates spatial arrangements built from two types of golden rhombohedra. These three-dimensional rhombic units are the building blocks for various polyhedral forms and aperiodic space-filling systems. The golden ratio governs the proportions of both unit types, linking their geometry to five-fold symmetry.
Different combinations of these rhombohedra create distinct geometric configurations. One assembly produces the rhombic triacontahedron, while alternative arrangements generate additional polyhedral forms. Each configuration shows how the same fundamental units organize into distinct spatial structures depending on orientation and packing sequence.
A further extension addresses three-dimensional aperiodic tilings, examining how golden rhombohedra fill space without periodic repetition. These arrangements maintain geometric coherence while avoiding translational symmetry, creating ordered structures that differ from conventional crystal patterns. Different assembly methods affect the resulting spatial organizations and their geometric properties. The investigation remains ongoing.
Photography: Phillip C. Reiner
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