Dui occupies the southeast in the Earlier Heaven arrangement attributed to Fuxi, directly opposite Gen in the northwest, since that order is built on exact opposition. In the Later Heaven arrangement attributed to King Wen, the order used in almost all applied practice, Dui moves to the west.
The move is not arbitrary. Later Heaven is organised by the seasonal cycle, and the west is autumn, the season of harvest and of what has been gathered in. A trigram whose attribute is the lake, the standing water that collects and holds, sits naturally at the point of the year when things are brought in rather than put out. That is the kind of reasoning the Later Heaven order runs on, and it is why the arrangement rather than the trigram carries the direction.
In the Later Heaven order Dui belongs to the phase Metal, shared with Qian, and to mid autumn. From the Shuogua, the Discussion of the Trigrams, Dui takes the sheep among animals and the mouth among the parts of the body, which fits an attribute already glossed as the Joyous, since the mouth is where speech and pleasure both come out. In the family scheme Dui is the youngest daughter, holding its single yin line in the top place.
A reader working from a diagram found without a caption should establish which of the two orders it uses before drawing any conclusion from where Dui appears on it.
Sources Fathoming the Cosmos and Ordering the World: The Yijing (I Ching, or Classic of Changes) and Its Evolution in ChinaRichard J. Smith with The I Ching, or Book of ChangesRichard Wilhelm (trans.); Cary F. Baynes (English trans.), The Five "Confucian" ClassicsMichael Nylan