3-D

Origami Hyperbolic Plane

Neil Calkin

Origami Hyperbolic Plane   by Neil Calkin

The hyperbolic plane was one of the first non-Euclidean geometries to be discovered in the 19th century. However, even the two dimensional hyperbolic plane is hard to represent: it doesn't fit well into the three dimensional real world. Various ways have been found to represent it: this model is the equivalent for the hyperbolic plane of the soccer ball representation of the sphere: it consists of regular heptagons (seven sided polygons, the central one made of orange, the others from all red modules) surrounded by regular hexagons (alternating blue with red or orange).

The model is robust, and is designed to be a hands-on, tactile model of (a portion of) a hyperbolic plane. Previous models have been built from cutout pieces of card, but the flexibility of heptagons made out of Tom Hull's PhiZZ units gives this model greater range of motion and allows it to be manipulated and (gently) handled.

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