S. Guttman et al. (2016) How faceted liquid droplets grow tails, PNAS 113:493 is an interesting paper by colleagues from Bar Ilan University that was presented by Dr. Eli Sloutskin at a conference in Israel which I attended. The authors show how oil droplets in water can take a polygon shape including the triangle and even the Star of David. This is due to entropic effects at the surface of the droplets. The shape of the polygons is dictated by topology, because there are 12 fivefold defects, as for the icosahedral droplets (the soccer ball shape). In all of these shapes the total order of defects is twelve.

In my opinion, it is completely amazing that geometry/topology dictates these shapes at such large length scales (50 microns or so) in comparison with the molecular size. Incredible that “geometry/information” affects “energy” at such large scales!

Below is Fig. 4 from the above mentioned paper. Complex shapes of liquid emulsion droplets.