Dissection of the path-simplex in Rn into n path-subsimplices

We review properties of acute and non-obtuse simplices, and of ortho-simplices and path-simplices. Dissection of path-simplices is considered, which leads to a new result: generalization of Coxeter’s trisection of a path-tetrahedron into three path-subtetrahedra to arbitrary spatial dimension n. Moreover, following earlier results by Korotov and Křížek, we show that applying this procedure recursively in the proper way leads to a self-similar path-simplicial refinement towards a chosen vertex of the original path-simplex.