The octagon is used as the symbol of the Ba Gua. This is in fact an accepted fallacy, a beautiful misunderstanding.

The Xian Tian Ba Gua was constructed according to the following description.

The Heaven and the Earth determine the positions. 
The Mountain and the Marsh can interchange qi.
The Thunder and the Wind echo.
The Water and the Fire do not assail each other.

It was just logical to visualize Heaven as above and Earth below. This determines the positions of the eight trigrams.

The other three opposite pairs are Mountain and Marsh, Thunder and Wind, Water and Fire.

The above diagram is quite symmetrical horizontally and vertically but not quite radially. Some artists thought that it would be more appealing to the eye if an octagon was used instead of the square. Thus the Ba Gua takes the shape of an octagon instead. However, it would have been more symmetrical if the circle was used to represent the Ba Gua and draw the trigrams with arcs instead of lines! The reason why this was not adopted was just because it was difficult to draw.

The Ba Gua is actually just a concept. The octagon is a pictorial representation of this concept. It could have been represented by a square or a circle. The octagon is not the Ba Gua and the Ba Gua is not an octagon.

The Hou Tian Ba Gua was derived from the Luo Shu which was a square divided into nine equal squares. This is used in Feng Shui studies as an energy map on a two dimensional surface.

If a "Ba Gua" is to be used to overlay on a floor plan to analyze the feng shui of a house the square is actually more convenient than the octagon. However, neither the square nor the octagon is the correct one to use. (See Lesson 9)

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