This paper explores the possibility of approximating asurface by atrihedral polygonal mesh plus some triangles at strategic places. The presented approximation has attractive properties. It turns out that the Z-coordinates} of the vertices are completely governed by the Z-coordinates assigned to four selected ones. This allows describing the spatial polygonal mesh with just its 2D projection plus the heights of four vertices. As aconsequence, these projections essentially capture the spatial meaning of the given surface, in the sense that, whatever spatial interpretations are drawn from them, they all exhibit essentially the same shape.