A Fairburn agate and a Waterline agate

Image from the whatsthisrock subreddit, where this is identified as a Fairburn agate ("the rarest agate in the world").  More info from Wikipedia -

"Fairburn Agate is a type of gemstone found in the agate beds of southwestern South Dakota and northwestern Nebraska. It is also the state gemstone of South Dakota. Fairburns are characterized from other types of agate by their colors and the shape of the bands... fortification banding distinguishes fairburns from other agate types. Fortification banding means that the concentric layers have sharp changes in direction which cause the bands to form angles in ways which are especially distinguishable from other agate types."

An illustration of the fortification banding -

As a child I spent inordinate amounts of time searching for agates in Minnesota.  I still have a jarful in the garage that I've never polished.  Here's another spectacular agate posted at whatsthisrock:

"Beautiful “Waterline Agate” as they are commonly called. The combination of the concentrically banded agate bordering the waterline agate complimented by the pocket with botryoidal chalcedony is absolutely stunning. This is a beautiful expression of the mineral quartz."