nowadays, when people need precision to 1/100th of an "inch" (250μm in modern units) on soft materials like unhardened steel, they can use steel tools
but when they need precision of 1μm or better (in medieval units, 1/25000th of an "inch"), or when they're cutting materials harder than steel, they resort to grinding with stone, typically emery (sapphire) for most of the grinding, followed by polishing. poor people who don't have steel tools also commonly do this for lower-precision work in soft materials; you can find all kinds of videos on youtube of people using angle grinders for things that a well-equipped machine shop would do with a bandsaw or milling machine
similarly, to get the dimensional references to measure to, common shop work can use cast-iron straight edges. but, for more precise work, they resort to granite surface plates
the egyptians of the old kingdom clearly had granite surface plates (they built significant parts of the pyramids' interiors out of them) and grinding, though they were evidently using the inferior quartz sand as their abrasive
as for symmetry, the most likely explanation is that they used lathes; the oldest indisputable records of lathes are from new kingdom egypt, but rotationally symmetric work that seems to have been made on a lathe appears as far back as the old kingdom
with respect to granite, while i don't doubt that you can find a granite vase here and there, most ancient egyptian fine stone carvings are from much softer rocks such as schist, alabaster (gypsum), and "alabaster" (calcite)
so i would say the investigation has already been done and found convincing answers
but when they need precision of 1μm or better (in medieval units, 1/25000th of an "inch"), or when they're cutting materials harder than steel, they resort to grinding with stone, typically emery (sapphire) for most of the grinding, followed by polishing. poor people who don't have steel tools also commonly do this for lower-precision work in soft materials; you can find all kinds of videos on youtube of people using angle grinders for things that a well-equipped machine shop would do with a bandsaw or milling machine
similarly, to get the dimensional references to measure to, common shop work can use cast-iron straight edges. but, for more precise work, they resort to granite surface plates
the egyptians of the old kingdom clearly had granite surface plates (they built significant parts of the pyramids' interiors out of them) and grinding, though they were evidently using the inferior quartz sand as their abrasive
as for symmetry, the most likely explanation is that they used lathes; the oldest indisputable records of lathes are from new kingdom egypt, but rotationally symmetric work that seems to have been made on a lathe appears as far back as the old kingdom
with respect to granite, while i don't doubt that you can find a granite vase here and there, most ancient egyptian fine stone carvings are from much softer rocks such as schist, alabaster (gypsum), and "alabaster" (calcite)
so i would say the investigation has already been done and found convincing answers