TITLE A Lower Bound for the Simplexity of the N-Cube via Hyperbolic Volumes AUTHOR Warren D. Smith, NECI, June 1998 ABSTRACT Let $T(n)$ denote the number of $n$-simplices in a minimum cardinality decomposition of the $n$-cube into $n$-simplices. For $n \ge 1$ we show that $T(n) \ge H(n)$, where $H(n)$ is the ratio of the hyperbolic volume of the ideal cube to the ideal regular simplex. $H(n) \ge \frac{1}{2} \cdot 6^{n/2} (n + 1)^{- \frac{n+1}{2}} n!$. Also $\lim_{n \to \infty} \sqrt{n} [ H(n) ]^{1/n} = 0.9281...$. Explicit bounds for $T(n)$ are tabulated for $n \le 10$, and we mention some other results on hyperbolic volumes. KEYWORDS Hyperbolic volumes, simplexity, triangulations, asymptotics.