The sum of its angles, derived from the formula (n-2)180°, is equal to 1080°.
Since there are eight equal angles in a regular octagon, each angle is equal to 1080°/n; where n is equal to 8 (the number of sides of the octagon).
1080°/n = 1080°/8
= 135° (an obtuse angle)
The eight angles of the regular octagon are the following eight directions of an 8-point compass rose (the eight-pointed star): north, east, west, south, north-east, north-west, south-east and south-west.
This means that the regular octagon is the geometric representation of a compass.
In Chinese Cosmology, Bagua (heaven) is an octagon. We know that heaven is the celestial sphere, which means that Bagua is an octagonal representation of the celestial sphere. The celestial sphere, with the cubicle representing the holy city, and the eight directions of the compass are the eight edges of the cube.
Note that an octagon can either be regular or irregular. Though a regular octagon represents balance, peace and harmony, an irregular octagon means conflict and chaos. Unlike a regular octagon, one or more angles and sides of an irregular octagon are different.
The term balance here implies equality between people of different religions, race, tribe, nation and language.
The most kept secret is that the world is a white light and diversity is a rainbow. We all constitute a white light and the diverse colours constituting the rainbow are products of a discriminating medium placed on our path.
White light is heaven. The light is a rainbow on earth because it is separated into the constituent colours of the rainbow by a glass ceiling placed between heaven earth.
Divided, the world is broken and the octagon is Yin or 2 (even number). United, the world is unbroken and the octagon is Yang or 1 (odd number).
This means that Bagua could either manifest as Yin or Yang. Yin is the sky of the underworld and Yang is the sky of the world above.
Yin = 'Yin Yang' (polarity or judgement)
Yang = Yinyang (neutrality or non-judgment)
Judgement or Yin is the irregular octagon symbolising a compass pointing downwards to the south (the ancient world). Non-judgment or Yang is the regular octagon symbolising a compass pointing upwards to the north (heaven or paradise).