Abstract
A cube tiling of eight-dimensional space in which no pair of cubes share a complete common seven-dimensional face is constructed. Together with a result of Perron, this shows that the first dimension in which such a tiling can exist is seven or eight.
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Mackey A Cube Tiling of Dimension Eight with No Facesharing. Discrete Comput Geom 28, 275–279 (2002). https://doi.org/10.1007/s00454-002-2801-9
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DOI: https://doi.org/10.1007/s00454-002-2801-9