When using the Hexpress grid generator one gets hexahedral cells, possibly with hanging nodes. Because of a smoothing step, the hanging nodes can be shifted: they are not necessarily on the straight line that connects the corners, as shown below.
With FVM one would triangulate the face with 5 nodes in order to approximate its surface, face center and such, see for example the book by Ferziger and Peric, Computational Methods for Fluid Dynamics, Springer, 2001. How should one treat this situation in FEM? I'm familiar with the hexa 8 mapping to a master element using linear shape functions but that doesn't seem quite enough.