Figure 1 is described in detail in my article in the Mathematical Gazette, XIX, No. 236. it is based on a tetrahedron ABCD and an arbitrary point D2. These five points determine all the other points of the figure, and if the tetrahedron ABCD is taken as the tetrahedron of reference and the coordinates of D2 are (α0, β0, γ0, δ0), the coordinates of A1, B1, C1, D1 are (- α0, β0, γ0, δ0), (α0,β0,-γ0, δ0), and so on. in what follows the tetrahedron A1B1C1D1 is called the associated tetrahedron.