if it's properly polished and not lazily done you can get a coin to shine like a mirror like this one.
There are two distinct ways that I could tell that this coin had been polished. The first would be lack of luster; on a coin with original surfaces, if you rotate the coin in light you should see 2 radial lines "cartwheel" around the coin. This is from the way the metal flows when it gets struck, creating an effect that can't be seen on coins that had their surfaces altered. On your
Indian Head cent, if you rotated it in the light you'll probably find that either all of the light reflects back to you, or none of it reflects back to you, it's a very unnatural effect and you can compare it to any modern cent you have to see what it's supposed to look like.
The Second is the shine on the high points of wear; once the coin gets worn, the luster is removed, so if you find a coin that is perfectly shiny but has signs indicative of wear, then you can suspect that it's been cleaned. Your
Indian cent has flat spots on the high points that even a weak strike wouldn't be able to explain (The high points in the leaves, the area where the headband meets the har, etc.) so it wouldn't make sense for the coin to have luster there if it's been worn, but it does.