Goshiki
This is probably the most diverse Koi variety known. Goshiki, meaning "five colored" in Japanese, are said to be five-colored Koi, although sometimes you'd be hard pressed to pick out the red, black, white, light blue, and dark blue color tones that are said to be available. Even further, a sixth color - purple - is formed when black and blue overlay one another.
Goshiki have strong Asagi lineage, which lends a reticulation to some or all of the scales. The traditional Goshiki is a rather dark fish, with messy, indistinct patterning, sometimes relieved by clear patches of hi, especially on the face and back. Others look like straight Kohaku and Asagi crosses, with a black, netlike reticulation covering the whole body. Certain examples of Goshiki can be absolutely breath-taking.
Gin-Rin Goshiki and Doitsu Goshiki add even more complexity to an already fathomless variety. Because the appearance of the reflective scales is influenced by the skin colors beneath, they can appear gold, silver, or bluish gray in a good Gin-Rin Goshiki. Often these combine in a single fish and the effect is almost unreal.