Although interstellar grains are known to be aspherical , their actual shapes remain poorly constrained .
We assess whether three distributions of ellipsoidal shapes from the literature , employed principally for their convenient mathematical properties , are suitable for describing the shapes of interstellar grains .
Randomly-selected shapes from each distribution are shown as illustrations .
The often-used BHCDE distribution includes a very large fraction of extreme shapes : fully 10 % of random draws have axial ratio a _ { 3 } / a _ { 1 } > 19.7 , and 5 % have a _ { 3 } / a _ { 1 } > 33 .
Of the three distributions considered , the CDE2 appears to be most realistic .
For each of the three CDEs considered , we derive shape-averaged cross sections for extinction and polarization .
Finally , we describe a method for “ synthesizing ” a dielectric function for an assumed shape or shape distribution if the actual absorption cross sections per grain volume are known from observations .
This synthetic dielectric function predicts the wavelength dependence of polarization , which can then be compared to observations to constrain the grain shape .