Alexandrov's generalization of Cauchy's rigidity theorem

The following is Theorem 27.2 of Igor Pak's book Lectures on Discrete and Polyhedral Geometry (which in general is a very nice resource for these sorts of questions):

Let $P,Q\subset\mathbb{R}^d$ (or $P,Q \subset S^d_+$), $d\geq3$ be two combinatorially equivalent (spherical) convex polyhedra whose corresponding facets are isometric. Then $P$ and $Q$ are isometric.

(Here $S^d_+$ is a d-dimensional hemisphere.)

This may help:

Bauer, C. "Infinitesimal Rigidity of Convex Polytopes." Discrete Comput Geom (1999) 22: 177. https://doi.org/10.1007/PL00009453

"Aleksandrov [1] proved that a simple convex $d$-dimensional polytope, $d \ge 3$, is infinitesimally rigid if the volumes of its facets satisfy a certain assumption of stationarity. We extend this result..."

[1] is the 1958 Convex Polyhedra book.

Wikipedia is correct. This is discussed in Alexandrov's book "Convex polyhedra" in Section 3.6.5.