DredNicolson's Quick Tips #2
A fake triangle is a quad face with a double vertex.
A fake triangle has a different origin/pivot point and behaves differently under subsurfing. A real triangle subsurfs into a rounded egg shape; a fake triangle retains a sharp point at the double vertex for a teardrop shape.
Fake triangles make it easier to accurately model objects with sharp points, like horns or the spikey tips of anime hair. Four fake triangles converging to a point form a 0-area quad face, or quadrupel vert.
When working with fake triangles, be careful about using the Remove Doubles tool, lest you turn them all into real ones. One precaution is to put intentional double verts into a vertex group, and deselect that group before removing accidental doubles. (Hit Z for wireframe mode and C for brush select to ensure you get all verts at the same spot.)
*Blender subsurfing. Depending on how they handle smooth subdivision, other 3D packages may give different results.