Abstract
We prove that a point in the Euclidean space R5 cannot be surrounded by a finite number of acute simplices. This fact implies that there does not exist a face-to-face partition of R5 into acute simplices. The existence of an acute simplicial partition of Rd for d > 5 is excluded by induction, but for d = 4 this is an open problem.
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Dedicated to Prof. Miroslav Fiedler on the occasion of his 80th birthday
An erratum to this article is available at http://dx.doi.org/10.1007/s00454-010-9267-y.
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Krizek, M. There Is No Face-to-Face Partition of R5 into Acute Simplices. Discrete Comput Geom 36, 381–390 (2006). https://doi.org/10.1007/s00454-006-1244-0
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DOI: https://doi.org/10.1007/s00454-006-1244-0