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A new research frontier for evolutionary 2D image generation is the use of mathematical models of aesthetics, with the goal of automatically evolving aesthetically pleasing images. This paper investigates the application of similar models of aesthetics towards the evolution of 3-dimensional structures. We extend existing models of aesthetics used for image evaluation to the 3D realm, by considering quantifiable properties of surface geometry. Analyses used include entropy, complexity, deviation from normality, 1/f noise, and symmetry. A new 3D L-system implementation promotes accurate analyses of surface features, as well as productive rule sets when used with genetic programming. Multi-objective evaluation reconciles multiple aesthetic criteria. Experiments resulted in the generation of many models that satisfied multiple criteria. A human survey was conducted, and survey takers showed a statistically significant preference for high-fitness highly-evolved models over low-fitness unevolved ones. This research shows that aesthetic evolution of 3D structures is a promising new research area for evolutionary design.