Geometry of PlayDome
The PlayDome is really a truncated icosahedron (or "half" of one anyway).
Imagine taking each tire and drawing lines tangent to the tread surface at
each bolt hole. These lines combine to create a pentagon around the small
tires, and a hexagon around the large tires. In its assembled state, the
vertices of the hexagons and pentagons (or triples of the tangent lines)
meet in the interior of the "equilateral triangle" gaps between the tires.
It is this observation that makes it clear why the circumferences of the
tires should be in a 6:5 ratio. Then the common "sides" of the imagined
pentagons and hexagons will be the same length.
This is the same idealized arrangement of the pure carbon molecule, C-60,
and is the same pattern employed for the panels of a soccer ball. There
are other geometric shapes that use just hexagons and pentagons, so
presumably one could create larger, non-spherical, structures based on the
same ideas.
Here are some sites that have information about fullerenes - larger
structures composed soley of hexagons and pentagons.
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Created: June 25, 1996, Updated: July 30, 1996.