The scientific name for this fossilized rock is hexagonaria percarinata. In Michigan, this gray rock is known as a Petoskey stone.
It is named for the city of Petoskey, Michigan, where many of the stones were found. The city was named for the Ottawa Indian chief Petosegay, meaning "Rays of the Rising Sun."
Although the chief was named before the stone, some find significance in the name. They suggest the fossilized coral polyps look like suns and the tentacles are their rays.
In 1965, Michigan declared the Petoskey Stone as its state stone. It became the first state to designate a fossil as its official state stone or rock.
Ella Jane Petoskey, the only living grandchild of Chief Pet-O-Sega, was present as the governor signed the bill.
Petoskey stones are softer than typical agates since they are fossils, rating a delicate 3-3.5 on the Mohs scale.
However, when you find them on the beach, they are very smooth because they have been naturally tumbled by rushing water, sand, and other stones.
Petoskeys can be hand-polished using sandpaper and corduroy. (You can explore page 4 of the linked PDF from the Michigan DEQ for step-by-step instructions.)
Where else can you find fossil agate coral? Florida's state stone, Agatized Coral, is another form.
Florida chose it in 1979; it is a form of silicified coral more similar to petrified wood. This is the only gemstone naturally found in Florida and can be located near Tampa Bay.