  The topological theory and the Volterra process are key tools for the
classification of defects in Condensed Mater Physics. We employ the same
methods to classify the 2D defects of a 4D maximally symmetric spacetime. These
\textit{cosmic forms}, which are continuous, fall into three classes: i)-
$m$-forms, akin to 3D space disclinations, analogous to Kibble's cosmic
strings; ii)- $t$-forms, related to hyperbolic rotations; iii)- $r$-forms,
never considered so far, related to null rotations. A detailed account of their
metrics is presented. There are \textit{wedge} forms, whose singularities
occupy a 2D world sheet, and \textit{twist} forms, whose singularities occupy a
3D world shell. $m$-forms are {compatible} with the cosmological principle of
\textit{space} homogeneity and isotropy, $t$- and $r$-forms demand
\textit{spacetime} homogeneity. $t$- and $r$-forms are typical of a vacuum
obeying the perfect cosmological principle in a de Sitter spacetime. Cosmic
forms may assemble into networks generating vanishing curvature.
