= Solution
For cubic <lattice planes>, $d_{hkl}=a/\sqrt{h^2+k^2+l^2}$. The <face-centred cubic selection rule> permits indices that are all odd or all even. Thus
$$
d_{111}=0.2336\,\mathrm{nm},\qquad d_{200}=0.2023\,\mathrm{nm},\qquad d_{220}=0.1430\,\mathrm{nm}.
$$
The first two spacings exceed the quoted 0.19 nm real-space resolution, whereas $d_{220}$ does not. This restriction is for the resolved image and its transform; a <diffraction> instrument need not have the same cutoff.
A natural candidate is a beam near a \b[local $\langle110\rangle$ <zone axis>]. For example, the $[110]$ <zone law> $h+k=0$ includes four $\{111\}$ reflections and two $\{200\}$ reflections, all within that real-space cutoff. Their reciprocal-space <length> ratio is $g_{200}/g_{111}=2/\sqrt3=1.1547$. The angle between $(1\bar11)$ and $(1\bar1\bar1)$ reciprocal vectors is $\cos^{-1}(1/3)=70.53^\circ$. In contrast, a $[001]$ view gives a fourfold arrangement of the resolvable $\{200\}$ family, while the lowest ordinary $[111]$ zone reflections are $\{220\}$ and would not be resolved at the stated cutoff.
In a five-domain decahedral interpretation, neighboring tetrahedral fcc regions meet on $\{111\}$ twin planes around a common near-$\langle110\rangle$ axis. Five unstrained wedges supply $5\times70.53^\circ=352.64^\circ$; elastic distortion accommodates the remaining $7.36^\circ$. Their rotated <diffraction> contributions need not resemble a single six-spot $[110]$ pattern. \b[Near-$\langle110\rangle$ fcc domains in a <multiply twinned particle> are a defensible orientation proposal, not a unique full indexing.] The printed transform has no reciprocal-space scale or indexed spot list, so it cannot establish every domain rotation or exclude an overlapping-particle contribution. Calibrated spacings and transforms from individual regions would settle those distinctions. The five-domain geometry is independently observed in atomic-resolution gold-particle measurements.<Study of Nanoparticles at UTSA: One Year of Using the First JEM-ARM200F Installed in USA by Alvaro Mayoral and others>[printed p.2, Fig.1 and accompanying discussion of decahedral gold and angular deficit]{ref}
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