The constructions given above, in terms of Clifford algebra or representation theory, can be thought of as defining spinors as geometric objects in zero-dimensional space-time. To obtain the spinors of physics, such as the Dirac spinor, one extends the construction to obtain a spin structure on 4-dimensional space-time (Minkowski space). Effectively, one starts with the tangent manifold of space-time, each point of which is a 4-dimensional vector space with SO(3,1) symmetry, and then builds the spin group at each point. The neighborhoods of points are endowed with concepts of smoothness and differentiability: the standard construction is one of a fiber bundle, the fibers of which are affine spaces transforming under the spin group. After constructing the fiber bundle, one may then consider differential equations, such as the Dirac equation, or the Weyl equation on the fiber bundle. These equations (Dirac or Weyl) have solutions that are plane waves, having symmetries characteristic of the fibers, i.e. having the symmetries of spinors, as obtained from the (zero-dimensional) Clifford algebra/spin representation theory described above. Such plane-wave solutions (or other solutions) of the differential equations can then properly be called fermions ; fermions have the algebraic qualities of spinors. By general convention, the terms "fermion" and "spinor" are often used interchangeably in physics, as synonyms of one-another.