  It is natural to regulate an infinite-sized system by imposing a boundary
condition at finite distance, placing the system in a "box." This breaks
symmetries, though the breaking is small when the box is large. One should thus
be able to obtain the asymptotic symmetries of the infinite system by studying
regulated systems. We provide concrete examples in the context of
Einstein-Hilbert gravity (with negative or zero cosmological constant) by
showing in 4 or more dimensions how the Anti-de Sitter and Poincar\'e
asymptotic symmetries can be extracted from gravity in a spherical box with
Dirichlet boundary conditions. In 2+1 dimensions we obtain the full
double-Virasoro algebra of asymptotic symmetries for AdS$_3$ and,
correspondingly, the full Bondi-Metzner-Sachs (BMS) algebra for asymptotically
flat space. In higher dimensions, a related approach may continue to be useful
for constructing a good asymptotically flat phase space with BMS asymptotic
symmetries.
