Complex sentence: The method uses the concept of a simplex, which is a polytope of "N" + 1 vertices in "N" dimensions; a line segment on a line, a triangle on a plane, a tetrahedron in three-dimensional space and so forth.
Split into simpler sentences: The method uses the concept of a simplex, which is a polytope of "N" + 1 vertices in "N" dimensions. Examples of simplexes include a line segment on a line, a triangle on a plane, a tetrahedron in three-dimensional space and so forth.