Problem 660

Erdős Problem #660: declared status 'open'. Formalized: no. Let $x_1,\ldots,x_n\in \mathbb{R}^3$ be the vertices of a convex polyhedron. Are there at least$$(1-o(1))\frac{n}{2}$$many distinct distances between the $x_i$? Prize: no. Tags: convex, distances, geometry.