Cubes of integral vectors in dimension four
Emil W. Kiss, P\'eter Kutas

TL;DR
This paper characterizes and counts m-icubes in four-dimensional integer space using Hurwitz quaternions, demonstrating the possibility of infinite extension of such structures.
Contribution
It provides a comprehensive description and enumeration of m-icubes in b4^4, and proves that they can be extended infinitely.
Findings
Describes m-icubes in b4^4 for 2 d7 m d7 4 using Hurwitz quaternions
Counts the number of m-icubes with a given edge length
Proves that m-icubes can be extended infinitely in b4^4
Abstract
A system of nonzero vectors in is called an -icube if they are pairwise orthogonal and have the same length. The paper describes -icubes in for using Hurwitz integral quaternions, counts the number of them with given edge length, and proves that unlimited extension is possible in .
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