  The crumpling of a thin sheet can be understood as the condensation of
elastic energy into a network of ridges which meet in vertices. Elastic energy
condensation should occur in response to compressive strain in elastic objects
of any dimension greater than 1. We study elastic energy condensation
numerically in 2-dimensional elastic sheets embedded in spatial dimensions 3 or
4 and 3-dimensional elastic sheets embedded in spatial dimensions 4 and higher.
We represent a sheet as a lattice of nodes with an appropriate energy
functional to impart stretching and bending rigidity. Minimum energy
configurations are found for several different sets of boundary conditions. We
observe two distinct behaviors of local energy density fall-off away from
singular points, which we identify as cone scaling or ridge scaling. Using this
analysis we demonstrate that there are marked differences in the forms of
energy condensation depending on the embedding dimension.
