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From a pseudo-triangulation with $n$ tetrahedra $T$ of an arbitrary closedorientable connected 3-manifold (for short, {\em a 3D-space}) $M^3$, we presenta gem $J '$, inducing $\IS^3$, with the following characteristics: (a) itsnumber of vertices is O(n); (b) it has a set of $p$ pairwise disjoint couplesof vertices $\{u_i,v_i\}$, each named {\em a twistor}; (c) in the dual $(J')^\star$ of $J '$ a twistor becomes a pair of tetrahedra with an opposite pairof edges in common, and it is named {\em a hinge}; (d) in any embedding of $(J')^\star \subset \IS^3$, the $\epsilon$-neighborhood of each hinge is a solidtorus; (e) these $p$ solid tori are pairwise disjoint; (f) each twistorcontains the precise description on how to perform a specific surgery based ina Denh-Lickorish twist on the solid torus corresponding to it; (g) performingall these $p$ surgeries (at the level of the dual gems) we produce a gem $G '$with $|G '|=M^3$; (h) in $G '$ each such surgery is accomplished by theinterchange of a pair of neighbors in each pair of vertices: in particular,$|V(G ')=|V(J ')|$.  This is a new proof, {\em based on a linear polynomial algorithm}, of theclassical Theorem of Wallace (1960) and Lickorish (1962) that every 3D-spacehas a framed link presentation in $\IS^3$ and opens the way for an algorithmicmethod to actually obtaining the link by an $O(n^2)$-algorithm. This is thesubject of a companion paper soon to be released.

COMBINATORIAL DEHN–LICKORISH TWISTS AND FRAMED LINK PRESENTATIONS OF 3-MANIFOLDS REVISITED