This is the fruit of the European water chestnut, Trapa natans. Also known commonly as devil pods, they float and can be found up and down the Hudson and less frequently on area beaches. The plant is a fast spreading invasive. They have been used for food and medicinal purpose in Europe for 5000 years or more. Strangely, they are becoming rarer and rare there, while flourishing here.
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This work by Matthew Wills is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License.
Backyard and Beyond 
here’s an interesting article on the Water Chestnut:
http://www.dcnr.state.pa.us/forestry/invasivetutorial/water_chestnut.htm
Great post; I have found some remarkably symmetrical European water chestnut pods. The color and texture both remind me of medieval woodwork.
when I found my first ever water chestnut pod on the shore of Lake Ontario in New York, I thought it was a piece of plastic from a kids toy like a transformer or space alien!!! At least now I know what they are!!!
Mom found these along the Rappahannock River, Virginia, in 1944 and strung them as a one of the main decorations on my first Christmas tree. Pop was stationed at Quantico at the time. I still have the string of them as I celebrate my 73rd birthday in 2017!
Happy birthday!