  Isomorphs are lines in the density-temperature plane of certain
"strongly-correlating" or "Roskilde simple" liquids where two-point structure
and dynamics have been shown to be close to identical up to a scale
transformation. Here we consider such a liquid, a Lennard-Jones glassformer,
and investigate the behavior along isomorphs of higher-order structural and
dynamical correlations. We then consider an inverse power law reference system
mapped to the Lennard-Jones system [Pedersen et al., Phys. Rev. Lett. 105,
157801 (2010)]. Using the topological cluster classification to identify
higher-order structures, in both systems we find bicapped square anti-prisms,
which are known to be a locally favored structure in the Lennard-Jones
glassformer. The population of these locally favored structures is up to 80%
higher in the Lennard-Jones system than the equivalent inverse power law
system. The structural relaxation time of the two systems, on the other hand,
is almost identical, and the four-point dynamical susceptibility is marginally
higher in the inverse power law system. Upon cooling the lifetime of the
locally favored structures in the Lennard-Jones system are up to 40% higher
relative to the reference system.
