The author attempts to determine how much of the Ising ground state there is in the ground state of an Heisenberg antiferromagnetic. Square planar clusters of 5, 13 and 25 spins of ¹/₂ are considered, using approximate ground states chosen as a result of symmetry arguments. Various physical quantities, including bond energies which are more negative than those found with the corresponding Ising states, then become relatively easy to evaluate. The author concludes that the chosen states are better approximations than the Ising states. It seems that as the number of spins increases the probability of finding the Ising state tends to zero, while remaining the most probable state, in a site representation.