Counting triangle crossings and halving planes
Tamal K. Dey, Herbert Edelsbrunner · 1993
Every collection of t ≥ 2n2 triangles with a total of n vertices in R3 has Ω(t4/n6) crossing pairs. This implies that one of their edges meets Ω(t3/n6) of the triangles. From this it follows that n points in R3 have only O(8/3) halving planes.