ABSTRACT
The purpose of this chapter is to describe the objects used as examples in Chapter 22.
The symmetries of the three lattices are easily found. Since the bc lattice consists of all points 0, 1, 2, 3 and doesn’t distinguish + from −, its symmetries can achieve the full dihedral group of permutations of 0, 1, 2, 3 and also the interchange of + and −. They therefore constitute the doubled octad group (8◦:2). The nc lattice consists just of 0 and 2, whose symmetries effect 〈(02), (13), (+−)〉, determining the negative double tetrad group (4−:2). Finally, the symmetries of the fc lattice, whose points are those colored 0, effect only 〈(13), (+−)〉, so form the negative double dyad group (2−:2).
