Symmetry

The center of the polygon is the 'the point of departure, the first link in the ontological causal chain. As the geometric nucleus, it is the source and the fount of all axes. All symmetries converge on this point, the point of zero magnitude, occupying no space.

It is a unique point, remaining unaltered no matter what symmetrical function is executed. It is not repeated elsewhere in the pattern, nor does it change during rotation.

'Is it possible that a point has no dimension, except that it be a metaphysical point, and how can it occupy 'place' if space has not yet been created from its unfolding? Clearly there has to be a precise differentiation between physical and metaphysical, between idea and expression, yet both are embraced by one reality.

[8]

The super-structure of the polygon is, of course, the circle. Motifs based directly on star polygons owe their existence to a feature that they share with the regular convex polygons: all derive from sets of points equally distributed around the circumference of a circle. It is common knowledge that a circle is a polygon with an infinite number of sides. The circle 'clothes' the n-pointed star, and gives it the loci for expansion and extension.

In terms of symmetry, it has an infinite-fold rotational axis. And once its outline is super-imposed on the polygonal structure, a unity is obtained that reflects the unity of the original point. The circle is not only the perfect expression of justice - equality in all directions in a finite domain - but also the most beautiful parent of all the polygons, both containing and underlying them. Outside the concept of time, the circle has always been regarded as a symbol of eternity, without beginning and without end, just being.

[xvii]

The metaphor of the star pattern motif is repeated everywhere. The process, which involves the conjunction of forms and structures of similar configuration but diminishing scales actually lends itself to analysis by fractal geometry, which applies itself to the uncovering of the order concealed in an apparent chaos, a theme which informs the origin and nature of architectural poetics itself.

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