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Cosmic Forms

The continuous 1D defects of an isotropic homogeneous material in a flat 3D space are classified by the Volterra process construction method. We employ the same method to classify the continuous 2D defects of a vacuum in a 4D maximally symmetric spacetime. These so-called \textit{cosmic forms} fall into three classes: i)- $m$-forms, akin to 3D space disclinations, related to ordinary rotations, analogous to Kibble's global cosmic strings (except that being continuous any deficit angle is allowed); ii)- $t$-forms, related to Lorentz boosts (hyperbolic rotations); iii)- $r$-forms, never considered so far, related to null rotations. A detailed account of their metrics is presented. In each class, one distinguishes between wedge forms, whose singularities occupy a 2D world sheet, and twist or mixed forms, whose inner structure appears as a non-singular \textit{core} separated from the outer part by a 3D world shell with distributional curvature and/or torsion. Relaxation processes of the world shell involve new types of topological interactions between cosmic dislocations and cosmic disclinations. The resulting structures of the core region itself are not explored in this article.