Symmetry in the houtian bagua

(Click pictures to enlarge)

At first glance the houtian bagua 後天八卦trigram circle seems devoid of any symmetry. It seems as if the trigrams follow each other in a random order, and that there is no logic behind it. But if we look at the circle in the way we are taught in the Ten Wings, namely as an order linked with time, patterns start to emerge.

In the Ten Wings the trigrams are described in the sequence of the houtian circle, starting with Zhen and going clockwise, ending with Gen . The trigrams are supposed to follow each other in time – Zhen and Xun are linked with Spring and morning, Li and Kun with Summer and midday, Dui and Qian with Autumn and evening, and Kan and Gen with Winter and midnight. In time, the trigrams change in each other – Zhen changes in Xun, Xun changes in Li, etc.

We can mark these changes in every trigram. When Zhen changes in Xun, all three lines change. When Xun changes in Li, the lower and the middle line change, etc. We can mark the lines that are going to change in every trigram:

In Zhen 3 lines change to make Xun; in Xun 2 lines change to make Li; in Li 2 lines change to make Kun, etc. There is a balanced sequence in the amount of changing lines: 3 – 2 – 2 – 2 – 1 – 2 – 2 – 2. The major change takes place in Zhen: the start of a new year and a new day.

It seems as if the line created by the pair ZhenDui, the symbols of sunrise and sunset, divides the circle in half. The trigram pairs created in this way are each others pangtonggua 旁通卦 and fangua 反卦. A pangtonggua is the inverse of a trigram: a yin line becomes a yang line and vice-versa. A fangua is the trigram turned upside down.

Xun is the combined pangtonggua and fangua of Gen; Li is the ptg and fg of Kan (although the fg is not visible because the trigram is symmetrical); Kun is the ptg and fg of Qian; Dui is the ptg and fg of Zhen.

If I would switch the trigrams Zhen and Gen the circle would even be better: that way every trigram would be opposed to its ptg, and no fg would be necessary. Also the changing lines sequence would become more symmetrical: 1 – 2 – 2 – 2 – 1 – 2 – 2 – 2. It surely makes room for speculation…..

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