The SuperCube: A Modular System for Periodic and Bounded Assemblies, 2026

A wireframe SuperCube with shaded faces sits beside a square diagram with phi measurements.

The SuperCube is a modular geometric unit derived from the five-cube compound by means of Boolean subtraction. A tetrahedral interlocking mechanism enables a single unscaled component to produce periodic and bounded assemblies with icosahedral symmetry. This publication documents the derivation method, geometric properties, and transformation matrices. The fundamental configurations generate the complete structural hierarchy from the basic interlocking units through periodic and bounded assemblies with applications at scales ranging from handheld objects to architectural structures.

Two SuperCube units with dark and light gray faces connect at a vertex.
Line drawings show SuperCube geometry with labeled angles and a central polyhedron.
Three wireframe diagrams labeled A, B, and C show a five-cube compound and its Boolean subtraction derivatives.
Three wireframe diagrams show a SuperCube unit, its Boolean subtraction, and the resulting tetrahedral assembly.
Three wireframe diagrams show the SuperCube unit, a cube with a tetrahedron subtracted from its interior.
Three SuperCube diagrams show a 3D model, a 2D net with shaded triangles, and a wireframe view.
A large SuperCube sits above three smaller labeled assemblies of the same modular geometric unit.
Three wireframe diagrams of the SuperCube show a radial cluster, a shaded planar view, and a vertical prism.
Three SuperCube diagrams show a 3D view, a 2D net with gray shading, and a vertical assembly.
Four SuperCube diagrams show modular assemblies with solid and dashed lines.
A SuperCube assembly sits above three wireframe variants labeled B, C, and D.

Photography: Phillip C. Reiner
https://doi.org/10.1007/s00004-025-00859-3

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