Antarctic Halos at Casey Station 66°S on August 23, 2008 captured by Tom Delfatti. Image ©Tom Delfatti, shown with permission.
Plate shaped and column shaped ice crystals formed this display. Both types have identical interfacial angles, only the relative sizes of the their faces differ.
The different arcs, common and rare, labeled in the matching HaloSim ray tracing simulation owe as much to the orientations of the crystals as to their shapes. Aerodynamic drag forces orient the crystals, very precisely indeed in the best displays, as they drift downwards .
The great scientist Christiaan Huygens was the first to realize the crucial role of orientation. In 1662 he was thus able to quantitatively predict the appearance of sundogs and upper tangent arcs. Together with Descartes numerical description of the rainbow this represented the start of mathematical physics and our quantitative understanding of the evolving Universe.