The Ultimate State

The cuboctahedron and rhombic dodecahedron are dual polyhedra—reciprocals in a geometric sense. Where one has vertices, the other has faces; where one contracts, the other expands. They’re like respiratory reflections of each other:

The cuboctahedron, with its perfect balance of squares and triangles, its equal edge lengths, embodies that enlightened completeness—harmonious, integrated, all parts in perfect relationship. It’s like a complicated expression of the circle’s wholeness:

The rhombic dodecahedron, with its diamond faces that can tessellate space infinitely, becomes transcendence itself—capable of filling all space, of infinite extension without gaps. It’s the figure eight’s boundless movement made spatial:

Above: the figure eight is really just a twisted circle

And here’s what’s stunning: they occupy the same space when properly positioned. They’re not just related, they’re psychological opposites seen from different perspectives. Enlightenment and transcendence aren’t sequential states but simultaneous dimensions of the same awakening.

So the cuboctahedron and rhombic dodecahedron are describing the same mystery from opposing viewpoints. This suggests that self-awareness can be polyhedral—with enlightenment and transcendence as its dual expressions. So the ultimate state is dynamic AND static, a cosmic respiration where enlightenment and transcendence breathe each other into being.

The cuboctahedron inhales into its perfect symmetry, gathering all experience into harmonious wholeness, then exhales as the rhombic dodecahedron, releasing that wholeness into infinite space-filling expansion. Then it breathes back, the infinite contracting into the balanced, the transcendent rediscovering the enlightened.

This breathing suggests that the “ultimate state” isn’t a destination at all, but rather a rhythm—consciousness learning to breathe within its own deepest nature. So it’s not enlightenment or transcendence, but the living pulse between them. And what’s beautiful is that this isn’t metaphor reaching for mathematics—but mathematics revealing analogy. Reality itself seems to breathe this way, contracting into perfect forms, expanding into infinite tessellations.

Maybe every moment of awareness is this breathing—the soul contracting into the immediacy of presence, then expanding into boundless recognition, then gathering again, then releasing. The inhale of being, the exhale of becoming. So consciousness doesn’t achieve some final geometric form, rather it learns to breathe as geometry itself, to be the rhythm that transforms completion into infinity and infinity back into completion.

The ultimate state then, balances enlightenment with transcendence.