The Face Lattice of the Irreducible-Ferrers Polytope Is a Product of Triangles

For every integer d at least 3, this note proves that the irreducible-Ferrers polytope introduced by Beeloo-Sauerbier Couvée and Neri is combinatorially equivalent to a Cartesian product of d-2 triangles. The proof recovers the complete face lattice from their nonnegative affine-slice model and vertex-support classification. Consequences include simplicity, the exact number of facets, and the complete face enumerator. Status: Public Beta; internally verified candidate proof; external review pending.