  Comet 162P/Siding Spring is a large Jupiter-family comet with extensive
archival lightcurve data. We report new r-band nucleus lightcurves for this
comet, acquired in 2018, 2021 and 2022. With the addition of these lightcurves,
the phase angles at which the nucleus has been observed range from $0.39^\circ$
to $16.33^\circ$. We absolutely-calibrate the comet lightcurves to r-band
Pan-STARRS 1 magnitudes, and use these lightcurves to create a convex shape
model of the nucleus by convex lightcurve inversion. The best-fitting shape
model for 162P has axis ratios $a/b = 1.56$ and $b/c = 2.33$, sidereal period
$P = 32.864\pm0.001$ h, and a rotation pole oriented towards ecliptic longitude
$\lambda_E = 118^\circ \pm 26^\circ$ and latitude
$\beta_E=-50^\circ\pm21^\circ$. We constrain the possible nucleus elongation to
lie within $1.4 < a/b < 2.0$ and discuss tentative evidence that 162P may have
a bilobed structure. Using the shape model to correct the lightcurves for
rotational effects, we derive a linear phase function with slope
$\beta=0.051\pm0.002$ mag deg$^{-1}$ and intercept $H_r(1,1,0) = 13.86 \pm
0.02$ for 162P. We find no evidence that the nucleus exhibited an opposition
surge at phase angles down to 0.39$^\circ$. The challenges associated with
modelling the shapes of comet nuclei from lightcurves are highlighted, and we
comment on the extent to which we anticipate that LSST will alleviate these
challenges in the coming decade.
