I am looking for a triangulation of an $n$-dimensional simplex such that all sub-simplices are of comparable size, and are "as close as possible" to a regular simplex : the latter property could be formalized as "the minimum $n$-dimensional angle is bounded away from $0$, uniformly in the size of the triangulation". I have read that the Delaunay triangulation had this kind of properties, but I did not find quantitative results about it, like lower bounds on the minimum angle.

Thank you!