A ‘compass rose’ star in the circular Xiantian diagram

The circular Xiantian ('Before Heaven') diagram is an elegant arrangement of the 64 hexagrams in a circle based on the halving of the centre 'bull's-eye' into yin (black) and yang (white) semicircles. This halving is then repeated for a further five concentric circles outwards in progressively smaller slices until the circle is divided into 64 sectors in the outer circle. The inner circle represents the bottom line of the 64 hexagrams, 32 of which are yin and 32 yang. By the third circle outwards the eight trigrams are represented, and the circle is divided into eight sectors, meaning that the hexagrams are arranged in groups of eight having the same lower trigram. Such groups are sometimes referred to as 'one lower trigram and eight upper trigrams'. The sixth circle represents the top line of the 64 hexagrams, which alternates between yin and yang from hexagram to hexagram (see Yijing hexagram sequences). Hexagrams 1 and 2 are the all-white and all-black sectors, respectively, either side of the vertical in the top half.

What has not been noticed before is that this arrangement has within it a beautiful 'compass rose' star pattern. Below I have darkened the background Xiantian diagram and drawn the star on it in red, here shown with 32 points, which can be expanded to 64 with a further iteration:

I first noticed this star in 2003, when I saw a thumbnail-sized image of the Xiantian circle. The small scale enabled me to recognise the pattern, which I had never seen before when viewing the circle at normal page size. When I drew in the lines of the star I was quite taken aback by the stunning symmetries on the kite- and lozenge-shaped facets, as if it had been a rough stone that now sparkled like a cut sapphire. So far as I know, nothing like this has previously been described – there is no diagram resembling it in the 'Zhouyi Tushi Dadian' ('Encyclopedia of Zhouyi Diagrams.' Beijing: Zhongguo gongren chubanshe, 1994, 2 vols).

You may wish to view the basic eight-pointed star, and further expanded to a 16-pointed star; also the 32-pointed star as drawn on the original printed diagram and another version with a light background. I have also drawn it as a unicursal eight-pointed star and with superimposed square. More circular and rectangular Xiantian diagrams as printed in Chinese sources can be seen in the scans archive, and you might also be interested in my experiment to square the circle.

There is also a 'skewed star' to be seen: