Ice has a hexagonal molecular symmetry* and its crystals are mostly hexagonal prisms that vary in proportion or habit from long columns to thin plates**. Plates and columns may have different relative face sizes and their hexagonal end faces can be irregular. However, regardless their individual proportions, the angles between their faces are always the same. Without this constancy we would not have halos. Alternate prism side faces always incline at 60° to one another. The two prism end (or basal) faces always incline 90° to the six side faces. These two wedge angles each produce their own groups of halos. Cloud crystals are commonly aligned in particular ways. This is the result of air resistance acting on the crystals as they drift slowly downwards relative to air currents in the clouds. Plate crystals drift down like leaves. Their large faces are almost horizontal.    Columns align themselves with their long axes nearly horizontal. Each alignment favours certain light paths through the crystals and produces its own own family of halos. Crystal habits, wedge angles and alignments are the keys to understanding halos. *  Ordinary hexagonal ice (ice Ih) is the only stable form under ordinary cloud conditions. Cubic ice (ice Ic) might exist at very low temperatures (<-80C) and would form different halos. There is some lack of agreement on whether any halos from cubic ice have been seen.     **  Ordinary ice also forms pyramidal crystals. Snowflakes are large and complicated hexagonal symmetry crystals and do not form halos except for some sun pillars.

Column and plate crystals These crystals are 100 - 1500X larger (depending also on your monitor) than those in the clouds which produce halos.