Your stone is crystalline Calcite. Its outer shape got rounded smooth by tumbling around on the bottom of a fast-moving river for many-many years. Then it somehow got broken more-or-less in half, which exposes the distinctive identifying form of the Calcite crystals. I know about this because waaay back in my college years I was a Spelunker (cave-explorer), and I saw many broken Calcite stalagmites, which had that same distinctive "internal" crystalline structure.
There is an area near here that you can find those stones that are similar to your example. We, I refer to them as ''Indian Marbles'', though not actually used by the Native Americans. The ones that I have found, all have the similar structure of lines radiating out from the center. As mentioned in the sixth post, they are a type of calcite.