Triangulations of the cube into a minimal number of simplices without
additional vertices have been studied by several authors over the past decades.
For 3≤n≤7 this so-called simplexity of the unit cube In is now
known to be 5,16,67,308,1493, respectively. In this paper, we study
triangulations of In 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 n≥3 there is essentially
only one other nonobtuse triangulation of In, and give its explicit
construction. The number of nonobtuse simplices in this triangulation is equal
to the smallest integer larger than n!(e−2).Comment: 17 pages, 7 figure