Change in projected structure with change in view orientation. (Upper panel) Images of a 3D reconstruction of BPV (), projected on a regular grid at 3° intervals of θ and φ (ω always = 0°) within a half of the icosahedral asymmetric unit (represented by dots in the right half of the inset). This gallery demonstrates how small changes in viewing angle can produce dramatic differences in the projected views of a 600-Å-diameter particle. The magnitude of these differences is correlated with the change in view direction and with the size of the particle. Hence, a 3° change in view direction leads to more-pronounced differences in projection images for a larger particle (>600 Å) or less-pronounced differences for smaller particles (<600 Å). (Lower panel [corresponds to boxed region of inset]). Demonstration that projected views at θ,φ and θ,−φ are enantiomers related by a vertical line of mirror symmetry. Note that when φ = 0°, the particle itself is mirror symmetric about a central vertical line (true for all images in leftmost column of upper panel). All equatorial views give rise to mirror-symmetric images. An icosahedron has 15 equators, each of which encircles the icosahedron along a direction that follows adjacent symmetry axes. For example, the equator in the *xy* plane (θ always = 90°; φ varies between −180° and +180°) crosses, in order, the following symmetry axes: two-, five-, three-, two-, three-, five-, two-, five-, three-, two-, three-, and fivefold. Any view corresponding to a combination of θ and φ which lies on this equator will be a mirror-symmetric image with the mirror line parallel to the equator. For example, the bottom row of projected images in the upper panel (which represent some of the views along the *xy* equator) all exhibit horizontal lines of mirror symmetry. Projection views along strict symmetry axes are additionally unique because they exhibit *n* mirror lines, where *n* (= 2, 3, or 5) is the symmetry of the axis in view.

## PubMed Commons