A natural cycle, where a player achieves a regular cycle but in a certain order. The player must hit a single, a double, a triple, and a home run in that order. The order is more commonly known as the "natural order." This feat has only been accomplished a 15 times.
Much less common is the reverse natural cycle, which is just what it appears to be: a home run, a triple, a double and a single, in that order. This has happened five times and the players who performed the feat are listed among the others below.
League: American
League: National