= Solution
Three suitable examples are \b[<cubes> bounded mainly by $\{100\}$ <facets>, <octahedra> bounded by $\{111\}$ <facets>, and <truncated octahedra> bounded by both $\{111\}$ and $\{100\}$ <facets>]. These are crystallographically distinct shapes rather than three arbitrary rounded particle outlines.
At fixed volume the <thermodynamic equilibrium> shape minimizes $G_{\rm surf}=\sum_i\gamma_iA_i$, with an edge/corner correction when particles are very small. In the <Wulff construction>, <facet> support-plane distances scale as their interfacial free energies. <Silver>'s clean low-index energies, selective <adsorption> of <ligands> or ions, <solvent> <chemical potential> and possible support contact alter those energies. <Crystal twinning> and elastic <strain> can add further costs or stabilize multiply twinned forms. A face with slow attachment kinetics can also survive during growth even when that morphology is not the <thermodynamic equilibrium> Wulff shape. <Homogeneous nucleation> describes where nuclei form; it does not guarantee an <thermodynamic equilibrium> final shape.
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