ABSTRACT
In this chapter, the authors present the design of lattices within a simplex geometry. The procedure will work for any number of components, but the authors illustrate simplex lattice design only up to four ingredients, which form a three-dimensional tetrahedron. A lattice is an arrangement in space of isolated points in a regular pattern, such as atoms in a crystalline solid. The number of blends in a simplex lattice design depends on both the number of components (q) and the degree of the polynomial. The number of design points N in a simplex lattice depends only on the number of components q and the degree of polynomial m. An easy way to infer the degree is by the number of design points along the edges; when broken in half, the degree is two—whereas a fragmentation by thirds indicates a third-degree lattice.
