An essential aspect in the interaction between people and computers is the recognition of facial expressions. A key issue in this process is to select relevant features to classify facial expressions accurately. This study examines the selection of optimal geometric features to classify six basic facial expressions: happiness, sadness, surprise, fear, anger, and disgust. Inspired by the Facial Action Coding System (FACS) and the Moving Picture Experts Group 4th standard (MPEG-4), an initial set of 89 features was proposed. These features are normalized distances and angles in 2D and 3D computed from 22 facial landmarks. To select a minimum set of features with the maximum classification accuracy, two selection methods and four classifiers were tested. The first selection method, principal component analysis (PCA), obtained 39 features. The second selection method, a genetic algorithm (GA), obtained 47 features. The experiments ran on the Bosphorus and UIVBFED data sets with 86.62% and 93.92% median accuracy, respectively. Our main finding is that the reduced feature set obtained by the GA is the smallest in comparison with other methods of comparable accuracy. This has implications in reducing the time of recognition.