The octagon is an eight-sided figure.  it represents, regeneration, rebirth or renewal.  In churches and temples, a dome is often held up by an octagonal structure thereby squaring a circle which is another way of saying joining the physical to the spiritual.  In numerology, the number eight represents spiritual achievement or enlightenment after having passed through the seven stages of growth.  It represents completion in Buddhism.  To the Chinese, it is a symbol of good luck and completeness.  In Hebrew, it is the number of the Lord.  There are eight winds, four major, four minor, eight regions of the world and eight chakras.  In Taoism, there are eight immortals.  In Christianity, eight beatitudes.  In Plato's philosophy, there are eight spheres of different colors  surrounding the pillars of Heaven.