By George Hart for the Museum of Mathematics
This four inch diameter ball is a two-layer geodesic sphere. It has an outer layer of triangles connected with an inner layer of pentagons and hexagons, which is the structure of geodesic domes such as the Montreal Expo67 dome. The above design is unique, however, in that it is chiral, meaning it is different from its mirror image. If you have access to a 3D printing machine, you can build a copy of this structure from the .STL file available here.
Without a 3D printer, you can still build complex two-layer domes from commercial plastic components, by following the instructions here.
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