On Zlámal Minimum Angle Condition for the Longest-Edge n-Section Algorithm with n ≥ 4

In this note we analyse the classical longest-edge n-section algorithm applied to the simplicial partition in Rd, and prove that an infinite sequence of simplices violating the Zlamal minimum angle condition, often required in finite element analysis and computer graphics, is unavoidably produced if n ≥ 4. This result implies the fact that the number of different simplicial shapes produced by this version of n-section algorithms is always infinite for any n ≥ 4.