2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64727Let X^{circ} be the space of all labeled tetrahedra in P^{3}. In [BGS] we constructed a smooth symmetric compactification X-tilde of X^{circ}. In this article we show that the complement X-tilde smallsetminus X^{circ} is a divisor with normal crossings, and we compute the cohomology ring H^*(X-tilde;Q).Replaced with revised version (minor edits only)Algebraic Geometry14M99, 14M15text