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A new construction of the minimum-genus orientable surface on which the n-dimensional hypercube graph can be embedded is presented. Simultaneously, this gives a new proof of the formula for hypercube genus and also leads to novel 3D models of cubes of any dimension. Examples are presented.

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Hypercube Models via Genus Embeddings

  • 动态工具书词条

  • 发表日期：

    2026年

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  • Richard H. Hammack

摘要

A new construction of the minimum-genus orientable surface on which the n-dimensional hypercube graph can be embedded is presented. Simultaneously, this gives a new proof of the formula for hypercube genus and also leads to novel 3D models of cubes of any dimension. Examples are presented.