  I discuss a special class of singularities obtained as a natural
4-dimensional generalization of the conical singularity. Such singularities
(called quasiregular) are ruinous for the predictive force of general
relativity, so one often assumes (implicitly as a rule) that they can be
somehow excluded from the theory. In fact, however, attempts to do so (without
forbidding the singularities by fiat) have failed so far. It is advisable
therefore to explore the possibility that their existence is not prohibited
after all. I argue that quasiregular singularities, if allowed, may appear
either in situations where causality is endangered or in the early Universe. In
the latter case objects might appear strongly (though not quite) resembling
cosmic strings. Those objects would be observable and, moreover, it is not
impossible that we already do observe one.
