Starting to experiment with combinatorial packings by gluing particles together along their edges and finding a configuration with maximal ratio between the volume of the sum of the particles and the volume of the convex hull of the particles. Here are some examples.
ratio = 0.4500
Expanding the tree to two particles. There are only two admissible configurations with different ratios for two particles.
1. branch
ratio = 0.4
Ratios from left to right: 0.3857, 0.4045, 04075, 0.4372, 0.4015, 0.3724
2. branch
ratio = 0.4091
Ratios from left to right: 0.4045, 0.3971, 0.3803, 0.4075, 0.4372, 0.4015