Fig. 4: Packing of ordered arrangements of colloids.
From: A colloidal viewpoint on the sausage catastrophe and the finite sphere packing problem
Packing fraction ηch of clusters consisting of spheres enclosed within their convex hull as a function of the number of particles N for a planar arrangements, b regular and regularly truncated tetrahedra Tn, with n the number of particles removed from each vertex, c regular and regularly truncated octahedra On, and d for a range of irregularly truncated tetrahedra T, octahedra O and bipyramids B, as indicated in the legends in each panel. The orange line represents the packing fraction of the linear arrangement of spheres ηlin(N). In d, open symbols represent irregularly truncated tetrahedra and octahedra with ηch < ηlin (↓), while closed symbols indicate cases where ηch > ηlin (↑), including bipyramids. Each panel is accompanied by example clusters, where the original non-truncated configuration is shown with transparent spheres. Dotted arrow lines are used to facilitate the identification of certain clusters that are mentioned in the text.
