(Z,2R,3R,4aR,7R,12aS)-2,3,7,8,12,12a-Hexahydro-2,3-dimethoxy-2,3, 7-trimethyl-4aH-[1,4]dioxino[2,3-c]oxecin-5(11H)-one: A commensurate occupationally modulated structure revealing a condition for diffraction symmetry enhancement for non-parent reflections

(Z,2R,3R,4aR,7R,12aS)-2,3,7,8,12,12a-Hexahydro-2,3-dimethoxy-2,3, 7-trimethyl-4aH-[1,4]dioxino[2,3-c]oxecin-5(11H)-one (dengue) crystallizes in the space group P3₁ and approximates the conditions necessary for diffraction symmetry enhancement without twinning for the h - k ≠ 3N reflections. The structure may be described as an occupancy modulation of a 1:1 disordered P3₁21 parent structure with Z = 3 that would only contribute to the h - k = 3N reflections. The crystal studied was a 0.717 (2):0.283 twin, but also had a stacking fault that on average caused the (1 - p_j):p_j population ratio for the alternative orientations of ordered columns along the three non-equivalent screw axes (j = 1, 2 or 3) of P3₁ to be describable by p₁ = 0.068 (3), p₂ = p₃ = 0.960 (3). The effect of these stacking faults could be simulated using global parameters that modify an ordered prototype structure. The structure reveals that the ten-membered lactone ring incorporates a Z-configured double bond and that the methoxy-substituted stereogenic centers created during a trans-diol protection step each possess the R-configuration.