Structural constraints encode protein topography and genome organization in PaV. (a) The capsid of PaV is organized according to icosahedral symmetry as illustrated by its match to the superimposed icosahedron (red). The magenta points are additional constraints encoded by our theory and correspond to the outermost points of the best-fit array. They match to the tops of the trimeric protein spikes, which is striking given that these are not located on axes of icosahedral symmetry. (b) A cross-sectional view (52 Å thick) of the capsid, showing the locations of the best-fit array points relative to the protein container and its closely associated dsRNA cage (light yellow). (c)–(e) Close-ups of the two trimers bounded by the green rhomb in (a) together with an associated portion of the dodecahedral RNA cage viewed from (c) outside the particle, (d) the side and (e) inside the particle. The point array encodes constraints on the trimeric protein complex (orange and yellow points) and the relative sizes of the capsid and RNA cage. Strikingly, (predictive) green points map on the three-way junctions of this cage, and (predictive) blue points fit snugly into the minor grooves of the A-type RNA duplexes. Since the locations of all points are fixed by extended symmetry with respect to the outermost array points (magenta), this implies that protein topography and RNA organization are correlated by a geometric scaling principle that is encoded by extended icosahedral symmetry. For clarity, array points are shown here and throughout as spheres of 4.5 Å radius, colour coded by their radial positions. Note, the PaV crystal structure is the result of icosahedral symmetry averaging. This procedure does not assume any interdependence of molecules at different radial levels and does not alter the conclusions from the matching to the array described above.