  A theory in which points, lines, areas and volumes are on on the same footing
is investigated. All those geometric objects form a 16-dimensional manifold,
called C-space, which generalizes spacetime. In such higher dimensional space
fundamental interactions can be unified \` a la Kaluza-Klein. The ordinary,
4-dimensional, gravity and gauge fields are incorporated in the metric and spin
connection, whilst the conserved gauge charges are related to the isometries of
curved C-space. It is shown that a conserved generator of an isometry in
C-space contains a part with derivatives, which generalizes orbital angular
momentum, and a part with the generators of Clifford algebra, which generalizes
spin.
