Some remarks on triangulating a d-cube (Q917916)

This paper deals with vertex-preserving, facet-to-facet triangulations of the d-cube. After describing briefly the standard triangulation into the maximal number of d! simplices and a method of \textit{J. F. Sallee} [Discrete Math. 40, 81-86 (1982; Zbl 0483.52003)], the author presents a new method. For \(d\geq 6\), this needs fewer simplices than Sallee's method (for \(d\leq 5\), Sallee's method requires the smallest possible number of tiles). The paper concludes with some formulas connecting certain simplex numbers for arbitrary triangulations of the d-cube in dimensions \(2\leq d\leq 6\).