A product of the probabilities of each new F-block is accumulated. Concurrently, a product of the probabilities of the intersection blocks is accumulated. In the extension processes described below, a new stage will always begin when block probabilities have been defined on a frame which respects some of the symmetries of the lattice. The reason is that asymmetries may have been introduced by the extension process to that point. This is compensated for by averaging the estimates over the appropriate lattice symmetries, and then normalizing.
Extension continues with symmetrized block probabilities.
Below, two special cases of this extension process are discussed in detail. Numerical studies based on these extensions will then be presented. We use the following notation for particular frames on the hexagonal lattice. Frames consisting of cells in a closest-packed arrangement are denoted with a single subscript. A single cell is denoted .