All of my recent work, Passacaglia, and Tetras are constructed solely from combinations of the four triangular forms or tetrahedra: Alpha, Beta, Gamma and Delta. This operates similarly to the subliminal mathematics in music. It provides a formal cohesion and narrative for the work.
These specific tetrahedra combine in varying sets to build larger copies of themselves. For example 2 Betas, 1 Gamma and 4 Deltas can combine to build a larger Beta. Similarly, each tetrahedron contains substructures of smaller and smaller tetrahedrons, that develop almost fractally.
The tetrahedra have interesting and complex properties:
• They can be combined in patterns that fill 3D space without voids.
• These patterns are aperiodic. Unlike bricks, they cannot be assembled into a single, regular pattern that repeats. Instead they radiate out in varying angles and combinations.
• The ratios of the edges and the sizes of each tetrahedron are related by the Golden Mean.