Most nanoparticle synthesis methods result in nanoparticles bounded by low-index, low-energy faces such as the {111} or {100} atomic planes. This makes intuitive sense, as any high-energy face should grow itself out of existence, leaving particles bound by more stable faces. Unfortunately, particles with mostly low-energy surfaces contain a low percentage of atomic edge and corner sites. The synthetic method of Tian et al. produces particles capped by {730} faces, a surface structure that contains a relatively high density of atomic step edges (see the right panel of the figure). The authors calculated that 43% of the total number of surface atoms reside along steps, which can be compared to 6%, 13%, and 35% for 5-nm-diameter platinum cubes, spheres, and tetrahedral particles, respectively.

From this perspective article of David L Feldheim; the synthetic method of Tian et al in question is an electrochemical method (electrodeposition). Some of the particle shapes shown in the paper of Tian et al reminded me of the particle shapes seen in the simulations of Saswata Bhattacharyya et al (See pp.18-19 of this pdf file for example) — I will try and get a preprint of their paper uploaded on the net, and link here. Here is the draft of the paper by Saswata Bhattacharyya et al on roughening transitions.