Generative design of robots requires navigating a vast search-space, encompassing physical configurations and behavioural parameters. Evolutionary Algorithms (EAs) have shown promising results, but often converge prematurely to a small set of sub-optimal designs. Most EAs fail to maintain sufficient diversity in the population that would allow the discovery of distinct functional robots. To counter premature convergence, we introduce a superquadrics-based representation (SQs) for robot bodies. SQs are interpretable, compact and computationally efficient mathematical representations of 3D geometrical shapes that can be tuned to specific design-spaces. To encourage morphological diversity, we combine this representation with a quality-diversity (QD) algorithm (MAP-Elites). We compare SQs and Compositional Pattern Producing Networks representations as generators of morphologies, combining them with standard EAs and MAP-Elites. In two test environments, we find that using SQs to generate morphology in conjunction with the MAP-Elites algorithm reaches the highest QD-score across both environments, maximising diversity of design and functionality of generated robots. The findings highlight the benefits of using a compact and interpretable geometric representation for exploring a complex design-space and suggest that combining SQs with an explicit diversity mechanism increases the quality and number of designs generated.