Facet Shading
This shading is just a working hypothesis, that is not
usually used
Even when the illumination equation is applied at each point of the faceted
nature of the polygonal nature is still apparent. The issue is the dicontinuity
of normals !
To overcome this limitation normals are introduced at each vertex.

Usually different than the polygon normal

Used only for shading (not backface culling or other geometric computations)

Better approximates the "real" surface

Assumes the polygons were a piecewise approximation of the real surface
(C0)

Normals provide information about the tangent plane at each point (C1)

Usually the average of the tangent of the neighbour facets
 not always (real discontinuity or more straightforwards value (sphere for
instance).