  Conserved charges in theories with gauge symmetries are supported on
codimension-2 surfaces in the bulk. It has recently been suggested that various
classical formulations of gravity dynamics display different symmetries, and
paying attention to the maximal such symmetry could have important consequences
to further elucidate the quantization of gravity. After establishing an
algebraic off-shell derivation of the maximal closed subalgebra of the full
bulk diffeomorphisms in the presence of an isolated corner, we show how to
geometrically describe the latter and its embedding in spacetime, without
constraining the geometry away from the corner, such as by assuming a
foliation. The analysis encompasses arbitrary embedded surfaces, of generic
codimensions $k$. The resulting corner algebra ${\cal A}_k$, calling $S$ the
embedded surface and $M$ the bulk, is that of the group $(Diff(S)\ltimes
GL(k,\mathbb{R}))\ltimes \mathbb{R}^k$. This result is independent of any
dynamics or pseudo-Riemannian structure in the bulk. We then evaluate the
Noether charges of ${\cal A}_2$ for Einstein-Hilbert dynamics and show that the
Noether charge algebra gives a representation of the algebra ${\cal A}_2$, for
finite proper distance corners in the bulk.
