Line tangents to four triangles in three-dimensional space

Details Line tangents to four triangles in three-dimensional space Line tangents to four triangles in three-dimensional space

2005-02-27

arxiv.org/abs/math/0502564v2

Discrete and Computational Geometry, 37, No. 3, (2007), 369--380.

Mathematics

Metric Geometry

13 pages, added missing case in Lemma 5

Scientific paper

We investigate the lines tangent to four triangles in R^3. 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.

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