, Volume 28, Issue 2, pp 275-279
Date: 01 Aug 2002

A Cube Tiling of Dimension Eight with No Facesharing

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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.