Often it is convenient to join adjacent triangles that are coplanar
into a single *facet*. In this case, a polyhedral surface is the
union of finitely many planar polygonal regions; here the *faces*
are the maximal 2-dimensional planar subsets of the mapping, the
*edges* are the maximal 1-dimensional linear subsets of the
boundaries of the faces, and the *vertices* are the endpoints of the
edges. Regions that are not simply connected may be generated in this
way.

Since any plane polygonal region can be decomposed into triangles, there is no loss of generality in defining polyhedral surfaces in terms of triangles only, though it is often more convenient in practice to use arbitrary polygonal faces.

**See also:**

- Smooth surfaces

* 8/13/94 dpvc@geom.umn.edu -- *

*The Geometry Center*