Crystals of the recently published [Bolotina, Kirschbaum & Pinkerton (2005). Acta Cryst. B61, 577–584] triclinic (P\overline1) structure of 5-nitro-2,4-dihydro-1,2,4-triazol-3-one (α-NTO) occur as fourfold twins. There are Z′ = 4 independent molecules per asymmetric unit. We show that the structure contains layers with 2-periodic layer-group symmetry p21/b 1 (1). This symmetry is lost through the stacking of the layers, which is a possible explanation for Z′ = 4. A layer can assume four different but equivalent positions with respect to its nearest neighbor. Twinning arises through stacking faults and is an instructive example of the application of order–disorder theory using local symmetry operations. The near-neighbor relations between molecules remain unchanged through all twin boundaries. The four structures with maximum degree of order, one of which is the observed one, and the family reflections common to all domains are identified. Rods of weak diffuse scattering confirm the stacking model.