On generalized bisection of n-simplices

A generalized procedure of bisection of n-simplices is introduced, where the bisection point can be an (almost) arbitrary point at one of the longest edges. It is shown that nested sequences of simplices generated by successive generalized bisection converge to a singleton, and an exact bound of the convergence speed in terms of diameter reduction is given. For regular simplices, which mark the worst case, the edge lengths of each worst and best simplex generated by successive bisection are given up to depth n. For n = 2 and 3, the sequence of worst case diameters is provided until it is halved.