  This work arose from efforts to generalise the usual cubical boundary by
using different 'weights' for opposite faces, but still to obtain a chain
complex, and this method was found to generalise.
  We describe a variant of the classical singular homology theory, in which the
usual boundary (n-1)-cubes of each n-cube are replaced by combinations of
internal (n-1)-cubes parallel to the boundary. This defines a generalised
homology theory, but the usual singular homology can be recovered by taking the
quotient by the degenerate singular cubes.
