In the past decade, significant efforts have been made to describe fish-habitat associations. However, most studies have oversimplified actual connections between fish assemblages and their habitats by using univariate correlations. The purpose of this study was to identify the features of habitat forming corals that facilitate and influences assemblages of associated species such as fishes. For this we developed three-dimensional models of colonies of Acropora cervicornis to estimate geometry (length and height), structural complexity (i.e., volume, density of branches, etc.) and biological features of the colonies (i.e., live coral tissue, algae). We then correlated these colony characteristics with the associated fish assemblage using multivariate analyses. We found that geometry and complexity were better predictors of the structure of fish community, compared to other variables such as percentage of live coral tissue or algae. Combined, the geometry of each colony explained 40% of the variability of the fish assemblage structure associated with this coral species; 61% of the abundance and 69% of fish richness, respectively. Our study shows that three-dimensional reconstructions of discrete colonies of Acropora cervicornis provides a useful description of the colonial structural complexity and may explain a great deal of the variance in the structure of the associated coral reef fish community. This demonstration of the strongly trait-dependent ecosystem role of this threatened species has important implications for restoration and conservation efforts.