>>113542750 simplex = single point
1 simplex = a line segment. 2 points and 1 edge joining them
2 simplex = a triangle. 3 points, 3 edges joining each pair of them and 1 face filling the inside
3 simplex = a tetrahedron. 4 points, 6 edges joining each pair of them, 4 faces for each triplet of points and also 1 "cell" filling the inside
what is a 4 simplex is left as an exercise for the reader. note that 4 simplex cannot be realized as a subset of the three-dimensional space without the edges and faces intersecting.
