Line tangents to four triangles in three-dimensional space

Hervé Brönnimann, Sylvain Lazard, Olivier Devillers, and Frank Sottile.

We investigate the lines tangent to four triangles in R3. By a construction, there can be as many as 62 tangents. We show that there are at most 162 connected components of tangents, and at most 156 if the triangles are disjoint. In addition, if the triangles are in (algebraic) general position, then the number of tangents is finite and it is always even.
Companion web page.
Here are some pictures from this project:


The manuscript in postscript. In PDF.