Parhelia of oriented pyramidal crystals.
When ice crystals take shapes similar to that shown they can be oriented
and then produce exotic 'parhelia' very unlike the familiar sundogs
of ordinary plate crystals.
The display at left has crystal tilts of 1° (std deviation) and they
create many odd parhelia.
Rather poor crystal orientations can still produce parhelia arcs.
The crystals in the display at right had their tilts increased to
15° at right yet some parhelion arcs survive, particularly the extremely
bright and colourful 23° 'upper parhelion' above the sun.
The pyramidal parhelia are named after the equivalent circular halo
ray path but, like ordinary sundogs, they are not necessarily at that
distance from the sun. Thus, the uppermost arc is a 23° parhelion
but it lies above the 23° circular halo and its distance depends on
the solar elevation.
Simulation: sun centered fisheye with the sun 30° high. 50%
of crystals were randomly oriented in order to produce the 9,18 and
23° circular halos.