= Solution
For the common \b[$[111]$-axis zinc-blende GaAs wire], a representative cross-section is a faceted hexagon with low-index sidewalls, often described by $\{110\}$-type facets. The threefold crystallographic symmetry of a polar $[111]$ direction can make alternate facets inequivalent, so triangular or truncated-triangular sections are also possible. \b[The zinc-blende label alone does not fix a unique hexagon]: growth direction, termination, twins, surface chemistry and kinetic facet selection also matter.
The accompanying sketch shows a representative faceted section rather than a circular cylinder. Facets that advance slowly in their normal direction tend to remain exposed, so a kinetic growth shape need not be an equilibrium Wulff shape.
A simple cause of tapering is \b[continued radial <vapor–solid growth> on sidewalls while the tip grows axially]. A lower wire segment has been exposed to precursors for longer than a segment formed near the end of growth. For a roughly constant radial growth speed $v_r$, its radius gains about $v_r[t_{\rm end}-t_{\rm formation}(z)]$, giving a larger base. Substrate-fed species, changing catalyst size and droplet wetting can also contribute. Tapering is not proof that the original VLS droplet was wider at every earlier stage.
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