What kind of Seed/ Nut is This?

Beech nut?

I am showing my stupidity here…but haven’t lived in the northeast long enough to learn all my tree names. I found a bunch of these “nut shells” on my neighbor’s property when I went to feed their chickens while they were away. I forgot to ask what they were, so I’ll ask here.

Since Beech trees are abundant, I thought maybe a Beech nut although I don’t know what those are. Then I remembered back to when I used to hike to Mill Hill in my childhood and there was a lone chestnut tree up there and thought maybe this was a chestnut shell – I saw no sign of any chestnuts near these pods though.

Empty Shell of a- Chestnut?

I thought I’d get a photo of them just for fun. I suppose some animal had eaten what was once inside.