Do the faces of tri-linear hex elements have to be planar? Three nodes define a plane. If the fourth node does not lie on the plane, then the nodes are not planar and the face is not plane. In general, the geometry of element may not be convex. Will this cause problems in mapping the element to the unit cube? If I recall correctly, for non convex elements in 2D the mapping from global domain to the parent domain is not guaranteed to exist or be continuous. Will similar problems occur in 3D?
A follow up question: If the faces of tri-linear hex elements have to be planar, are they guaranteed to remain plane as the solution progresses when solving large deformation elasticity problems?