First the bright halos:
Touching the top of the circular 22° radius halo is an intense and sharp arc convex to the sun.  This is an upper tangent arc or, strictly speaking a circumscribed halo because the sun is just higher than the 29 degrees its name changes.  

Above that is a rarer arc but here almost equally bright – a suncave Parry arc.  

Both arcs are produced by similar ray paths through six sided, column shaped ice crystals drifting with their long axis oriented nearly horizontally.    Those making the tangent arc have all rotational positions about the long axis.   Those making the Parry arcs do not rotate but are instead most improbably oriented with two prism side faces horizontal.   The different crystal orientations dramatically change the halo produced.   

Another ice crystal habit, plates, made the prismatic sundog at right.

Now the fainter and much rarer halos:
An upper Lowitz arc stretches from the 22° halo, through the tangent arc to itself become tangent to the upper Parry arc.    Tobias Lowitz first drew one of the family of these arcs in 1790 at St Petersburg but they were not photographed until a few years ago.  

If a long sought Lowitz arc was not enough, an even rarer helic arc produced by reflection from the side faces of the Parry oriented crystals extends up from the sun, crossing the 22 degree and upper tangent arcs.