LONDON — As the group of amateur archaeologists sifted through tiles, animal teeth and pottery fragments buried within an ancient Roman pit in eastern England, one of them encountered something unusual last June.

It was a cast bronze object, hollow in the middle, flat along 12 faces, about the size of a clenched fist. Only one of the diggers — all members of Norton Disney village’s archaeology society — recognized the discovery: It was a Roman dodecahedron, likely to have been placed there 1,700 years earlier.