Tarrain with phong has artifacts

I threw together a pixelshader which does phong lighting.
The result was less than perfect though. As can be seenhere

Begin quite tired now with my brain might not be working right, I may just be stupid, but that was not what I expected. I did not expect to see all those pyramid shapes after doing the pr. pixel lighting.

I canculate the vertex normals as an unweighted average of the normals for all the triangles using the vertex. So for four triangles A,B,C,D meeting in a vertex I take the normal as
Vector3.Normalize(A.n+B.n+C.n+D.n)

What am I messing up here? I would like my terrain to look smooth right now, and without all those sharp edges.

Thanks in advance for any help you can provide.

[834 byte] By [ThomasGreenleaf] at [2007-12-23]