The use of deep learning to undertake shape analysis of the complexities of the human head holds great promise. However, there have traditionally been a number of barriers to accurate modelling, especially when operating on both a global and local level. In this work, we will discuss the application of the Swap Disentangled Variational Autoencoder (SD-VAE) with relevance to Crouzon, Apert and Muenke syndromes. Although syndrome classification is performed on the entire mesh, it is also possible, for the first time, to analyse the influence of each region of the head on the syndromic phenotype. By manipulating specific parameters of the generative model, and producing procedure-specific new shapes, it is also possible to simulate the outcome of a range of craniofacial surgical procedures. This opens new avenues to advance diagnosis, aids surgical planning and allows for the objective evaluation of surgical outcomes.