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Koi (鯉?, English /ˈkɔɪ/, Japanese: [koꜜi]) or more specifically nishikigoi (錦鯉, [niɕi̥kiꜜɡo.i], literally "brocaded carp"), are a group of fish that are ornamental varieties of domesticated common carp (Cyprinus carpio) that are kept for decorative purposes in outdoor koi ponds or water gardens.

Photo of six different types of Koi.
Etymology
The word koi comes from Japanese, simply meaning "carp." It includes both the dull grey fish and the brightly colored varieties. What are known as koi in English are referred to more specifically as nishikigoi in Japan (literally meaning "brocaded carp"). In Japanese, koi is a homophone for another word that means "affection" or "love"; koi are therefore symbols of love and friendship in Japan.

Differences from goldfish

Koi have prominent barbels on the lip that are not visible in goldfish.
Goldfish were developed in China more than a thousand years ago by selectively breeding Prussian carp for color mutations. By the Song dynasty (960–1279), yellow, orange, white, and red-and-white colorations had been developed. Goldfish (Carassius auratus) and Prussian carp (Carassius gibelio) are now considered different species. Goldfish were introduced to Japan in the 16th century and to Europe in the 17th century. Koi, on the other hand, were developed from common carp in Japan in the 1820s. Koi are domesticated common carp (Cyprinus carpio) that are selected or culled for color; they are not a different species but a subspecies, and will revert to the original coloration within a few generations if allowed to breed freely.

In general, goldfish tend to be smaller than koi, and have a greater variety of body shapes and fin and tail configurations. Koi varieties tend to have a common body shape, but have a greater variety of coloration and color patterns. They also have prominent barbels on the lip. Some goldfish varieties, such as the common goldfish, comet goldfish, and shubunkin have body shapes and coloration that are similar to koi, and can be difficult to tell apart from koi when immature. Since goldfish and koi were developed from different species of carp, even though they can interbreed, their offspring are sterile.
via Wikipedia (EN)

饲养在水池中的金鱼群正在游动
via Wikipedia (CN)