2D cell shape index distributions.

(a) The distribution of 2D shape index, p2D, in slices from 3D cell packings provide a signature of the 3D shape index, p3D. p3D values vary from 5.4 (solid black) to 6.4 (dashed red) in increments of 0.2. (Data available online [33].) (Inset) The location of the distribution peak varies smoothly with p3D. (b) The p2D-distribution tail decays with a similar form for all values of p3D. Example cross sections illustrate that arbitrarily large p2D values can be produced when the cross section is nearly parallel to a nearby edge—this produces nearly-rectangular slim shapes, for which p2D diverges when the cutting plane is near the edge. In contrast, general cross sections near a vertex are triangles, and the shape index, which is insensitive to the size of the triangle, retains a constant value independent of proximity of the cutting plane and vertex.