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<p>The SuperCube is a modular geometric unit that enables periodic and bounded assemblies with icosahedral symmetry through a tetrahedral interlocking mechanism. Derived from the five-cube compound through Boolean subtraction, this component produces diverse spatial forms from a single unscaled unit. The systematic development presented here documents the derivation method, geometric properties, and transformation matrices. Fundamental configurations generate the complete structural hierarchy, from basic interlocking units to periodic, bounded, and extended assemblies, with practical applications from handheld to architectural scales.</p>

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The SuperCube: A Modular System for Periodic and Bounded Assemblies

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月12日

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  • Phillip C. Reiner

摘要

The SuperCube is a modular geometric unit that enables periodic and bounded assemblies with icosahedral symmetry through a tetrahedral interlocking mechanism. Derived from the five-cube compound through Boolean subtraction, this component produces diverse spatial forms from a single unscaled unit. The systematic development presented here documents the derivation method, geometric properties, and transformation matrices. Fundamental configurations generate the complete structural hierarchy, from basic interlocking units to periodic, bounded, and extended assemblies, with practical applications from handheld to architectural scales.