The Voronoi tasselation consists in partitioning the plane into regions based on the distance to points in a specific subset of the plane.
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.
Given points, withlinearly 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