My take on the idea of a cathedral, on architecture of churches is narrow and simple: geometry. I called it Geometry of Transcendence. I explore geometric shapes in architecture, specifically the view of the dome inside of a cathedral.
The circle as a perfect geometric shape represents perfection, eternity, and the heavens. The square is associated with the physical nature of a human world. There are geometric shapes in between the circle and the square: convex polygons like octagon or star polygons like eight-pointed star, made from rotated square, inscribed within a circle. These middle shapes are symbolic of earthly existence basking in divine spirit or transcendence of a human soul on a way to the heaven.
Beyond the spiritual meaning of these geometric shapes there is a simple fact these are all symmetrical objects. Symmetry is hardwired in our brains as the most harmonious, beautiful and proportional arrangement, it gives us a sense of order and balance. Simply stated, it is a pleasurable experience to observe symmetry in our world. We humans enjoy symmetry on a deep unconscious level. It is a gift we have.