Full diallels involve all the possible combinations of crosses among parents, including
reciprocals and self-fertilization of the parents (if that is possible). For a sample of n parents, the full-diallel requires n x n crosses, a number that quickly becomes unmanageable as more parents are sampled.
Half diallels: Each parent is mated once with every other parent, excluding selfs and reciprocals. This requires making n(n-1)/2 crosses for n parents.