A master face is a face image that passes face-based identity authentication for a high percentage of the population. These faces can be used to impersonate, with a high probability of success, any user, without having access to any user information. We optimize these faces for 2D and 3D face verification models, by using an evolutionary algorithm in the latent embedding space of the StyleGAN face generator. For 2D face verification, multiple evolutionary strategies are compared, and we propose a novel approach that employs a neural network to direct the search toward promising samples, without adding fitness evaluations. The results we present demonstrate that it is possible to obtain a considerable coverage of the identities in the LFW or RFW datasets with less than 10 master faces, for six leading deep face recognition systems. In 3D, we generate faces using the 2D StyleGAN2 generator and predict a 3D structure using a deep 3D face reconstruction network. When employing two different 3D face recognition systems, we are able to obtain a coverage of 40%-50%. Additionally, we present the generation of paired 2D RGB and 3D master faces, which simultaneously match 2D and 3D models with high impersonation rates.