Beholder

Beholder

Visual musings on the mathematical and existential matter of infinity: like love, it’s in the eye of the beholder. Table of diagrams on right from Don Hatch’s amazing website on tessellations and other sundries.

Schlafli and Wythoff symbols, enough equations to boondoggle the mind. Wikipedia entry on uniform tilings on the hyperbolic plane:

There are an infinite number of uniform tilings on the hyperbolic plane based on the (p q r) where 1/p + 1/q + 1/r < 1, where p,q,r are each orders of reflection symmetry at three points of the fundamental domain triangle – the symmetry group is a hyperbolic triangle group.

In Hatch’s diagrams on the right, you can see the various tessellations (as depicted on a Poincaré disk surface) transform as different values are inputted — up to infinity in the bottom right corner.

Print available on Etsy.

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