A Cube Tiling of Dimension Eight with No Facesharing (original) (raw)

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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.

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1. Department of Mathematics, Harvard University, One Oxford Street, Cambridge, MA 02138, USA jfm@math.harvard.edu, USA
   Mackey

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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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• Published: 01 August 2002
• Issue date: August 2002
• DOI: https://doi.org/10.1007/s00454-002-2801-9