|Florida Pyramidal Halos imaged near Ft. Lauderdale by Kate Horne May 29, 2009. ©Kate Horne, shown with permission.
Ordinary hexagonal ice crystals have faces always inclined at 0, 60, 90 and 120 degrees to each other. Rays passing between the 60 and 90 degree inclined faces of poorly oriented crystals produce the familiar 22° circular halo and the rare 46°.
When hexagonal ice crystals have pyramidal ends there are many more opportunities for halo formation. They can have up to 20 faces inclined at 'wedge angles' of 28, 52, 56, 60, 62, 64, 80 and 90 degrees. The result - a number of so called "odd-radius" halos.
Here the inner halo is 18° in radius from rays passing between faces inclined at 52° (ray paths like 13-25, see here for face numbers).
Further out there are traces of a 20° halo.
Beyond that is a characteristic jumble of halos of radius 22,23 and 24°.
There was probably a 9° halo too but the lower cloud and tree obscured that.
Pyramidal crystals form more halos when they are partially oriented.
Crystal face angles are not arbitrary. They form in directions corresponding to well populated planes of atoms in the crystal lattice and always make the same angles to each other.
Everyday ice with its hexagonal structure could theoretically form crystals with other sets of angles. They can easily be calculated but would be unusual. Halos from them have not been observed with the possible exception of the enigmatic elliptical halos.