KöMaL 2026 B5525

For edge $e$ in tetrahedron $T$ let us define quantity $r(e)$ as the ratio of the distance of the two heights of the tetrahedron from the endpoints of e and the length of edge $e$. Let $R(T)$ be defined as the sum of $r(e)$ for all the edges of tetrahedron $T$. Show an example for a tetrahedron $T$ for which $R(T)>5.999$.