The mapping of phenotype onto genotype for a set of functional model proteins is accomplished by exhaustive enumeration on a three-dimensional diamond lattice. Chains of up to 25 monomers are investigated and their evolution characterized. The model is used to investigate the origins of designability. Highly designable functional model protein structures possess contact maps that have a relatively little commonality with other physically allowed contact maps. Although the diamond lattice has the same coordination number as the square lattice, differences between three-dimensional and two-dimensional functional model proteins are observed. One difference is the lower frequency of structures of low designability on the three-dimensional lattice. In other respects, the conclusions drawn from previous studies using the square lattice remain valid in three dimensions. For example, we observe the tendency for longer chains to form larger networks of sequences with greater stability to mutation. We identify various topographical characteristics of the landscapes: evolutionary bottlenecks bridge otherwise unconnected networks, and hub sequences allow rapid movement between the different neutral networks. The diversity of landscapes that arises from even a minimalist model suggests that real proteins have a rich variety of evolutionary landscapes. (C) 2003 American Institute of Physics.