  Tailoring the specific stacking sequences (polytypes) of layered materials
represents a powerful strategy to identify and design novel physical
properties. While nanostructures built upon transition-metal dichalcogenides
(TMDs) with either the 2H or 3R crystalline phases have been routinely studied,
our knowledge of those based on mixed 2H/3R polytypes is far more limited. Here
we report on the characterization of mixed 2H/3R free-standing WS$_2$
nanostructures displaying a flower-like configuration by means of advanced
transmission electron microscopy. We correlate their rich variety of
shape-morphology combinations with relevant local electronic properties such as
their edge, surface, and bulk plasmons. Electron energy-loss spectroscopy
combined with machine learning reveals that the 2H/3R polytype displays an
indirect band gap with $E_{\rm BG}=1.6^{+0.3}_{-0.2}~{\rm eV}$. Further, we
identify the presence of energy-gain peaks in the EEL spectra characterized by
a gain-to-loss ratio $I_G/I_L>1$. Such property could be exploited to develop
novel cooling strategies for atomically thin TMD nanostructures and devices
built upon them. Our results represent a stepping stone towards an improved
understanding of TMDs nanostructures based on mixed crystalline phases.
