In the last decade, three-dimensional landmarking has gained attention for different applications, such as face recognition for both identification of suspects and authentication, facial expression recognition, corrective and aesthetic surgery, syndrome study and diagnosis. This work focuses on the last one by proposing a geometrically-based landmark extraction algorithm aimed at diagnosing syndromes on babies before their birth. Pivotal role in this activity is the support provided by physicians and 3D ultrasound tools for working on real faces. In particular, the landmarking algorithm here proposed only relies on descriptors coming from Differential Geometry (Gaussian, mean, and principal curvatures, derivatives, coefficients of first and second fundamental forms, Shape and Curvedness indexes) and is tested on nine facial point clouds referred to nine babies taken by a three-dimensional ultrasound tool at different weeks' gestation. The results obtained, validated with the support of four practitioners, show that the localization is quite accurate. All errors lie in the range between 0 and 3.5 mm and the mean distance for each shell is in the range between 0.6 and 1.6 mm. The landmarks showing the highest errors are the ones belonging to the mouth region. Instead, the most precise landmark is the pronasal, on the nose tip, with a mean distance of 0.55 mm. Relying on current literature, this study is something missing in the state-of-the-art of the field, as present facial studies on 3D ultrasound do not work on automatic landmarking yet.