  The theory of defects in ordered and ill-ordered media is a well-advanced
part of condensed matter physics. Concepts developed in this field also occur
in the study of spacetime singularities, namely: i)- the topological theory of
quantized defects (Kibble's cosmic strings) and ii)- the Volterra process for
continuous defects, used to classify the Poincar\'e symmetry breakings. We
reassess the classification of Minkowski spacetime defects in the same
theoretical frame, starting from the conjecture that these defects fall into
two classes, as on they relate to massive particles or to radiation. This we
justify on the empirical evidence of the Hubble's expansion. We introduce
timelike and null congruences of geodesics treated as ordered media, viz.
'm'-crystals of massive particles and 'r'-crystals of massless particles, with
parallel 4-momenta in M^4. Classifying their defects (or 'forms') we find (i)
'm'- and 'r'- Volterra continuous line defects and (ii) quantized topologically
stable 'r'-defects, these latter forms being of various dimensionalities.
Besides these 'perfect' forms, there are 'imperfect' disclinations that bound
misorientation walls in three dimensions. We also speculate on the possible
relation of these forms with the large-scale structure of the Universe.
