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- W2951652780 abstract "Triangulations of the cube into a minimal number of simplices without additional vertices have been studied by several authors over the past decades. For $3leq nleq 7$ this so-called simplexity of the unit cube $I^n$ is now known to be $5,16,67,308,1493$, respectively. In this paper, we study triangulations of $I^n$ with simplices that only have nonobtuse dihedral angles. A trivial example is the standard triangulation into $n!$ simplices. In this paper we show that, surprisingly, for each $ngeq 3$ there is essentially only one other nonobtuse triangulation of $I^n$, and give its explicit construction. The number of nonobtuse simplices in this triangulation is equal to the smallest integer larger than $n!({rm e}-2)$." @default.
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- W2951652780 date "2012-09-18" @default.
- W2951652780 modified "2023-09-27" @default.
- W2951652780 title "There are only two nonobtuse binary triangulations of the unit $n$-cube" @default.
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