Among different recent technologies proposed for human face classification and recognition, solutions based on analyzing the 3D geometric facial features emerged as a promising academic and practical direction. Researchers have examined both holistic and local approaches to analyzing the 3D face regions to study the impact of facial features in real-life applications such as medical and security implementations. However, a few works have investigated the relevant impact of the extracted geometric features from the descriptive local regions of the human face on identifying human ethnicity. This work proposes a classifier to categorize individuals into their distinctive ethnic groups and deeply analyzes the facial feature variations to highlight the most descriptive parts and features of the human face in race classification. The proposed ML-based classifier is preceded by extracting the 3D facial features from 3D meshes using the recent SIFT and Geodesic distance calculations. In addition, it implements and discusses the initial important preprocessing steps including, cropping the frontal parts, correcting the head pose, selecting the suitable initial key points, aligning the 3D meshes, and implementing the suitable template-based 3D registration. The proposed NN race classifiers are built and evaluated using Headspace, a well-known multi-ethnic dataset, and achieved high accuracy (90% globally, and 100% for the mouth area) especially while using the SIFT features.