A Cube Tiling of Dimension Eight with No Facesharing
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- Mackey Discrete Comput Geom (2002) 28: 275. doi:10.1007/s00454-002-2801-9
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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.