# How to determine the outward normal vector of a face of a hexahedron if the orientation (CW or CCW) of vertices of the face is unknown

Consider a single quadrilaterally-faced hexahedron. If given the co-ordinates of the vertices, $\mathbf{v}_i$, of a face in counter-clockwise orientation, I can compute the corresponding unit outward normal vector using a cross-product:

$\mathbf{n}=\frac{(\mathbf{v}_2-\mathbf{v}_1)\times(\mathbf{v}_4-\mathbf{v}_1)}{\parallel(\mathbf{v}_2-\mathbf{v}_1)\times(\mathbf{v}_4-\mathbf{v}_1)\parallel}$

However, consider now an arbitrarily shaped volume which is discretised into a large number of quadrilaterally-faced hexahedra. Consider in particular a face shared by two adjacent hexahedra. If now given the co-ordinates of the vertices of the face in a certain orientation, the orientation will be clockwise for one hexahedron and counter-clockwise for the other.

If I do not know the orientation beforehand, how can I ensure that the unit normal is pointing outwards (assuming you know the co-ordinates of all vertices of all faces of all hexehedra)?