The lattice
design is a type of
Mixture Design that has points
at the corners (single components) and along
each side (equal proportions of two components).
The augmented lattice has additional points
in the interior representing mixtures that
use all three components:
Note that a mixture design
can have any number of constituents but
it is convenient to illustrate the design
as a mixture with three ingredients. This
gives a triangle in which each corner represents
one of the ingredients.
