The Buckeye "fruit", so to speak, is unusual. The seed pods it creates are spiked and vary in size and content. In early September, 2017, we visited the grove and found one of the Buckeye trees had some seed pods. A small pod disconnected from the tree at a slight touch. It opened easily had one small seed in it:
A larger pod (the one in the top photo, actually) was tougher to get off the tree and had to be opened with a pen knife. It contained two much larger seeds:
With two seeds crammed into a pod, the seeds are less round. You can see how they flatten against one another. The tree gets its name from the seed appearing as a the eye of a buck (male deer), which you can certainly see in the photo of the smaller seed.