Discrete & Computational Geometry

, Volume 28, Issue 2, pp 275–279

A Cube Tiling of Dimension Eight with No Facesharing


DOI: 10.1007/s00454-002-2801-9

Cite this article as:
Mackey Discrete Comput Geom (2002) 28: 275. doi:10.1007/s00454-002-2801-9


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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© Springer-Verlag New York Inc. 2002

Authors and Affiliations

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

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