For each point, there is a region of all points closer to it than any other one (Voronoi cells).
A simplex is the generalisation of a triangle/tetrahedron to an arbitrary number of dimensions. The k simplex is a k-dimensional polytope, the convex hull of its k+1 vertices.
linearly independent, the simplex determined by them is the set of points
- the 2-simplex is a triangle;
- the 3-simplex is a tetrahedron;
- the 4-simplex is a 5-cell