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Face recognition is a widely accepted biometric verification tool, as the face contains a lot of information about the identity of a person. In this study, a 2-step neural-based pipeline is presented for matching 3D facial shape to multiple DNA-related properties (sex, age, BMI and genomic background). The first step consists of a triplet loss-based metric learner that compresses facial shape into a lower dimensional embedding while preserving information about the property of interest. Most studies in the field of metric learning have only focused on 2D Euclidean data. In this work, geometric deep learning is employed to learn directly from 3D facial meshes. To this end, spiral convolutions are used along with a novel mesh-sampling scheme that retains uniformly sampled 3D points at different levels of resolution. The second step is a multi-biometric fusion by a fully connected neural network. The network takes an ensemble of embeddings and property labels as input and returns genuine and imposter scores. Since embeddings are accepted as an input, there is no need to train classifiers for the different properties and available data can be used more efficiently. Results obtained by a 10-fold cross-validation for biometric verification show that combining multiple properties leads to stronger biometric systems. Furthermore, the proposed neural-based pipeline outperforms a linear baseline, which consists of principal component analysis, followed by classification with linear support vector machines and a Naive Bayes-based score-fuser.