'Taisho Sanshoku', or 'Sanke' is the term applied to a koi that has a white body with red and black markings. The black markings are in the form of spots that are generally confined to the body above the lateral line.
Appreciating a Sanke is the same as those of a Kohaku, with the addition of its black markings. It is said that a good Sanke is actually a good Kohaku that has been further enhanced by black spots that add elegance to the koi. The sumi of a sanke must be distributed in the koi body. Their presence should enhance the 'kohaku pattern' and not degrade it. The red-over-white pattern may be continuous or 'stepped', but the over-all effect of white and red balancing each other. Many people prefer stepped koi and understandably so, since this pattern ensures red and white alternating with each other. Sanke with a 'hi' pattern that runs continuously from head to tail is known as 'aka sanke'. Aka sanke is less desired, since the predominantly red body makes it look heavy.
A white area separating the tail and the red marking nearest the tail is known as a tail stop, and is considered desirable. A red mark on the lips of a koi (also known as 'kuchibeni') is a 'plus' if it enhances the over-all package of the koi. A good sanke has a red pattern (but absolutely no black color) on the head. The head pattern must extend slightly beyond the eyes but should not reach the nose or lips, leaving a white area in the front end of the head. A fully red head (referred to as 'menkaburi') that makes the koi look 'hooded' is considered negative. Nonetheless, some koi look good despite having it.
A single round patch of red on the head and nowhere else is a "Tancho Sanke", a highly-prized koi variety among the Japanese since it looks like their national bird. If there are other red markings on the body of the koi, then the round head patch makes it a 'maruten' sanke.
Im not a big lover of sanke I dont know why i just cant get excited over them!