A sundog is a rainbow-like spot in a cirrus cloud. Light shining through ice crystals in the cloud makes a sundog, much like light shining through raindrops makes a rainbow.
Ice can take on many forms and shapes.
The cloud ice, however, is shaped like hex bathroom tiles or stubby pencils each no bigger than the tiniest grains of sand. These ice crystals bend light like a prism, disperse its colors, and cause sundogs. When the crystals line up like tiles on a table, the light shining through makes sundogs. The horizontal crystals bend the light 22 degrees, say Lynch and Livingston, as the light enters and exits the crystal. Light colors fan out from the bending and display as a sundog.