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

A wireframe cube and square diagram show geometric angles and lengths using the golden ratio.

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

Two SuperCube units link at a vertex, showing dark gray and light gray tetrahedral faces.
Diagram A shows SuperCube folding steps and a spherical assembly, while Diagram B details geometric subdivisions.
The SuperCube uses a tetrahedral interlocking mechanism to form assemblies with icosahedral symmetry.
Three wireframe diagrams show the SuperCube's tetrahedral interlocking mechanism and modular assembly.
Three wireframe views labeled A, B, and C show the SuperCube unit with light and dark shaded faces.
Three SuperCube modular units display tetrahedral interlocking mechanisms in wireframe and shaded views.
The SuperCube (2026) by Phillip C. Reiner is a modular geometric unit derived from a five-cube compound via Boolean subtraction.
Three line drawings show the SuperCube modular unit in open, shaded, and closed states.
Three wireframe views show the SuperCube unit and its periodic assemblies.
Four diagrams show SuperCube modular units with tetrahedral interlocking mechanisms in different geometric assemblies.
A large SuperCube assembly sits above three smaller geometric models labeled B, C, and D.

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

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