What nut did I find? I ask this knowing that it's possibly borderline off-topic, but I don't see a Botany SE site where I could ask, so...

A few days ago I stumbled (literally) upon an odd little fruit that had fallen onto the sidewalk. It fascinated me because it had three large lobes and a hard, mottled outer texture. I couldn't figure out what it was, so I brought it home and promptly forgot about it for a couple days.



When I picked it up today, one lobe had softened, and with a little pressure I was able to pop it off. The lobe contained a smooth, dark-brown nut!





Upon examination this reminded me of a chestnut. I broke off another lobe and found a second pod:



I have no idea what these are; they appear very similar to chestnuts but are missing the pointed tip and spiny shell. I don't know what to make of them. 



Does anybody know what these are? More to the point for this site, are they (safely) edible? I noticed a lot more had fallen nearby, and I'm not above gathering some if they're tasty.
That is a buckeye, fruit of Aesculus glabra, also known as the Ohio buckeye tree. The seeds (the "buckeye" part) look sort of like a horse chestnut, but the fruit is different.

Do not eat it!


  The fruits contain tannic acid, and are poisonous to cattle, and humans, as is the foliage. (Wikipedia)


(You can, however, make buckeye candy: peanut butter balls dipped in chocolate.)

This is a buckeye still on the tree, as well as some leaves if you'd like to revisit the source to verify: