The binding energies of equivalent, symmetric lattices such as the thr
ee-dimensional f.c.c., b.c.c., simple-cubic and diamond structures, th
e two-dimensional hexagonal, square and graphite layers and the one-di
mensional linear chain are compared using a first-nearest-neighbour em
bedding potential for the bond order which retains the first term in a
recently derived many-atom expansion. Unexpectedly we find that the b
ond energy of angularly dependent sp-valent systems with identical dim
ensionality shows the same square-root dependence on coordination numb
er as that predicted by the conventional embedded atom potential or th
e angularly independent bond order potentials for s-valent systems. Th
us the inclusion of the predicted angular character in the first term
of the many-atom expansion for the bond order does not provide any add
itional differentiation between the binding energies of different isod
imensional structure types.