If the near perfect orientation of column crystals sounds improbable, that of Parry oriented crystals must seem wildly so. The long crystal c axis is horizontal AND so are two of the prism side faces. The only degree of freedom is the ability of the crystal to take all rotational positions about a vertical axis passing through the crystal centre and perpendicular to the two horizontal faces.

The resulting halos are called Parry arcs. They are named after the explorer William Edward Parry who first observed one of them. Some Parry arcs are not particularly rare and with careful observation will be seen a few times a year .

Rays passing through two prism side faces with a wedge of 60° produce sunvex and suncave Parry arcs (column orientations make tangent arcs). These are the most common Parry arcs.

Rays travelling between a side face and a vertical end face - wedge of 90° - make the exceeding rare Parry supralateral (Tape) and infralateral arcs. Rays passing between the horizontal and vertical faces make the circumzenithal and circumhorizon arcs much more commonly produced by plate crystals.

Reflection from a sloping prism face gives a very rare helic (heliac) arc until recently only seen in the Antarctic.