Hyperbolic Orthogonal Dodecahedrons

Posted by on Feb 20 2008 | projective geometry

Image:Hyperbolic orthogonal dodecahedral honeycomb.png

While investigating the connections between projective geometry and Einstein’s General Theory of Relativity, I came upon this beautiful diagram that shows an infinite network of interconnected dodecahedrons (12 pentagons). If we can imagine that space is in fact structured, then what might that structure look like? Apparently there are many interesting solutions. This diagram is far more regular (Euclidean) than any proposed by Einstein which would be warped by the matter that created them. Matter creates the structure of space and the structure of space only exists in its interrelationship with matter.

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