Robust and computationally efficient parametric geometry modeling is essential for aerodynamic shape optimization in preliminary design. Conventional CAD systems, based on high-precision NURBS representations used in detailed design, exhibit significant limitations in this context. This work presents a parametric geometry modeling approach based on subdivision surfaces for robust, gradient-based shape optimization of complex topologies. Using polygon meshes ensures simplicity and intuitive design manipulation. While geometric accuracy is lower than NURBS, subdivision surfaces offer superior robustness in handling shape variations, enabling stable geometry updates during optimization. Geometric sensitivities are computed accurately via algorithmic differentiation, eliminating inefficient finite-difference approximations or surrogate models and ensuring high-fidelity gradients. The approach is tailored for high-dimensional design spaces and supports efficient gradient-based optimization under numerous constraints. Intrinsic surface parameterization enables smooth mesh deformation and facilitates reuse of existing flow solutions, significantly reducing computational effort. Consistent mesh quality and topology preservation are maintained throughout the optimization process. The paper describes the core principles of the approach and presents first results from aerodynamic shape optimization, demonstrating its practical applicability.