I recently found a box of my late grandfather's personal effects. Inside were two coins; one was an 1887 U.S. Indian-head penny, and the other is this coin.
I scanned it, amped it up in Photoshop, so its qualities were visible. It is not in the best condition.
From the green on the coin, I think it is copper. The coin is 2.5 centimeters (1 inch) in diameter, with a thickness of 1/8". On both sides, there's a "beaded" rim embellishment. (You'll have to excuse my complete lack of coin knowledge and terminology.)
The obverse features a right-facing man with a beard. He looks a lot like Charles Darwin. His head is bare. He faces to the right of the screen (his left). There are words written around almost the entire perimeter of the coin, and these words are illegible. Where the guy's beard is, I think it reads DEI, and it - like the other words/letters, is upside-down. So it's probably words written in Latin. There may be an "M," a "P," another "P," and even an "S" included in the other letters, but this is pure speculation.
The reverse includes a crest: it's a shield with a round circle on it that contains a globe with what appears to be a spyglass on it (I can't remember the official word for "spyglass"). The shield has a rounded crown upon it. To the left of the shield and crown are two characters. The first is a 2 and the second is most probably a 0 (to make 20), but perhaps the second character is a C (to make 2C), or a 5 (to make 25). To the right of the shield/crest is one character: either an are or a P (capital letter). Or maybe this is the handle of a sword. But I think it's a letter.
I'm taking the chance that someone simply recognizes this coin by sight or description. If this is not the case, I can highlight whatever areas on the coin are necessary to lead to an identification. My spouse and I did a coin rub, and that didn't help. We put it under lights, over a lightbox, onto a stamp pad, and in a lemon-juice-soaked cloth - none of these things helped, either. I've searched on Google and Google Images for hours, and have found nothing helpful. Thank you very much in advance of your help.

Identified - moved to World Coins forum