In this work, we present a new versatile 3D multilinear statistical face model, based on a tensor factorisation of 3D face scans, that decomposes the shapes into person and expression subspaces. Investigation of the expression subspace reveals an inherent low-dimensional substructure, and further, a star-shaped structure. This is due to two novel findings. (1) Increasing the strength of one emotion approximately forms a linear trajectory in the subspace. (2) All these trajectories intersect at a single point - not at the neutral expression as assumed by almost all prior works-but at an apathetic expression. We utilise these structural findings by reparameterising the expression subspace by the fourth-order moment tensor centred at the point of apathy. We propose a 3D face reconstruction method from single or multiple 2D projections by assuming an uncalibrated projective camera model. The non-linearity caused by the perspective projection can be neatly included into the model. The proposed algorithm separates person and expression subspaces convincingly, and enables flexible, natural modelling of expressions for a wide variety of human faces. Applying the method on independent faces showed that morphing between different persons and expressions can be performed without strong deformations.