Getting mathematical: there are examples matching tetrahedron, cube, octahedron and dodecahedron, but not the icosahedron. But the first ball here shows that the makers are close to being able to “dualise”, so it’s plausible to me that they may have known the icosahedron-type arrangement.

The large discs on the ball in the first image match the faces of a cube; the knobs on the ball in the second image might match those of a dodecahedron.

Carved stone balls are uniquely Scottish artefacts from the late Neolithic (3000-2500 BCE). The decorations, often raised or inscribed knobs or discs, are in some cases configured in the same way as faces or vertices of polyhedra.

Scottish Neolithic carved stone ball. (Ashmolean museum AN1927.2727 or AN1927.2730) Carved from red stone, about the size of a tennis ball, and decorated with 6 large raised discs (arranged like the faces of a cube) and 8 raised triangles (arranged like the vertices of the cube).

Scottish Neolithic carved stone ball. (Ashmolean museum AN1927.2727 or AN1927.2730) Carved from pale stone, a bit smaller than a tennis ball, and decorated with raised knobs (possibly 12 of them arranged like the faces of a dodecahedron).

Visiting Oxford for a viva, and there’s time to look at some carved stone balls in the Ashmolean museum.