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arXiv · 1108.3113

Cubes of integral vectors in dimension four

Emil W. Kiss·Péter Kutas
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Abstract

A system of $m$ nonzero vectors in $\mathbb{Z}^n$ is called an $m$-icube if they are pairwise orthogonal and have the same length. The paper describes $m$-icubes in $\mathbb{Z}^4$ for $2\le m\le 4$ using Hurwitz integral quaternions, counts the number of them with given edge length, and proves that unlimited extension is possible in $\mathbb{Z}^4$.

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Emil W. Kiss, Péter Kutas. 2011-08-15. Cubes of integral vectors in dimension four. https://arxiv.org/abs/1108.3113

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