The mean first-nearest-neighbour coordination number N₁ of atoms in a cluster is an important parameter characteristic of cluster size and geometry. For metal clusters and catalysts, its value is directly measurable by EXAFS spectroscopy. Literature expressions for N₁ in clusters are not accurate; ideal values have previously had to be worked out numerically by counting atomic site types. New, rigorous analytical formulae for N₁ as a function of cluster edge length have now been derived for icosahedral and cuboctahedral geometries. For clusters of the same size, N₁(icos) always exceeds N₁(cuboct), by a factor which is greatest for small clusters. The value of N₁ has recently been proposed to play an important role in the non-metal–metal transition of mercury and other metal-atom clusters; it follows that an icosahedral cluster might be ‘more metallic’ than a cuboctahedral one with the same number of atoms, a consequence which should readily be testable experimentally. The use of the N₁ parameter also gives new insight into cluster growth mechanisms.