Neolithic Carved Stone Polyhedra
Hundreds of carved stone spheres, roughly three inches in diameter, believed to date to around 2000 BC, have been found in Scotland. Some are carved with lines corresponding to the edges of regular polyhedra. Roughly half have 6 knobs---like the one at right above---but the others range from three to 160 knobs. The more mathematically regular ones do not appear to have had a special importance. For example, in addition to the 12-knob dodecahedral form shown in the center and just to its right above, there are also ones with 14 knobs, corresponding to a form with two opposite hexagons, each surrounded by six pentagons. Nonetheless, the dodecahedron appears here long before the Greeks wrote of it. The function of these stones is unknown and so it is unclear whether I should list them here under the category art, but many are intricately carved with spirals or cross-hatching on the faces. The material varies from easily carved sandstone and serpentine to difficult, hard granite and quartzite.
The above image is by Keith Critchlow, scanned from the book by Lawlor. Both those authors lean towards the mystical and must be read critically. In the image, note that the third and fourth balls, with icosahedral and dodecahedral edges indicated, do not correspond to different underlying carvings. I don't know if there are any with exactly 20 knobs arranged as an icosahedron.
For a primary reference (but with
no mathematical
discussion) see Dorothy N. Marshall, "Carved
Stone Balls," Proceedings
of the Society of Antiquaries of Scotland 180, pp. 40-72,
1976/77.
Addendum 2009: Lieven le Bruyn has followed up on my comment above about the incorrect bands marking the icosahedral ball and discovered that in contradiction to the claim in Critchlow's book, the five balls in the image above are not the five balls in Oxford's Ashmolean Museum. Below are the five Ashmolean balls None of these have exactly 12 bumps, so none can be a dodecahedron:
Le
Bruyn suggests that Critchlow may have falsified or fabricated the
image he published. I see no reason to think Critchlow's
image is deliberately fabricated or falsified. Clearly Critchlow's
source for the image is not what his book states. The paper bands
are not mathematically consistent with the carving, and the suggestion
that they correspond to all five Platonic solids is wrong. But there is
no reason to think they are not actual neolithic stone balls in an
undoctored image. I assume Critchlow used five actual neolithic stone
balls for the image, but decorated them in a misleading manner, trying
to make too strong a point because of his leaning toward the mystical.
I assume they came from a different museum and his misstatement of the
source is likely to be a writing error. Further investigation to
clarify the source of the balls in Critchlow's image is certainly
warranted.