How can a vertex have a normal? I understand a normal to indicate the following information:


  normals are intersections which are perpendicular to the plane of your face


I understand this to be a vector. And that a shader uses this information to calculate how to render something to the screen. For instance, whether this plane would reflect light to the camera or not, which of course depends on its orientation. (Correct me if I am wrong).

Then I read that a vertex, by itself, can have normal data. This I do not understand. Maybe I completely miss the point and context, but: How can a single vertex, not being part of a line (or a plane), indicate a normal? I mean, a single vertex is dimensionless right. Would its normal not always come from the planes surrounding it? So it is more of a derived value, instead of an intrinsic value of the vertex itself?
The vertex normals will be the average of the adjacent faces' normals.
Look at the lower-right corner of the ear in each of the two head images showing &quot;face&quot; vs &quot;vertex&quot; normals:

Notice that the face normals from the image on the left, about the lower-right vertex, are moved and redrawn from that vertex on the image to the right.
I am not an expert in cgi but it is safe to assume that all normal vectors are the same size. A unit vector about the vertex can be found by adding the vectors tip-to-tail and dividing by the length. This unit vector would then be scaled up by whatever display length the user selected.