Well an update to the squished, pressed, or elongated coins. Apparently there are three machines in the American Museum of Natural History each with four designs.
The first four located inside the first floor gift shop includes the following design.

The second four are located outside the first floor museum gift shop.

Most of the images are from their dioramas, permanent exhibits, or the buildings themselves.
Again the value of each is about $0.50 which is also their price.
There are four more from the the machine outside the Dinostore located upstairs but I will get those on another day. For some reason I really like these coins, which is strange since I usually don't like altered coins.
Do you have a coin and want to know its value? Leave a comment/question and I will do my best to find out the price and history for you.