The picture below shows a couple of varieties that are upright growers...very indeterminate, and late maturity. These could be used in those potato boxes, towers, tire rings, etc.
The photo below shows the same varieties in the background but also shows a very different type of potato......brachytic with multiple stolons creating new vines far and away from the base tuber, still indeterminate but in a compact way, very long maturity. These also could be used in potato boxes, towers, tire rings, etc.
Both types of potatoes had to be killed by the frost and were grown in rectangular pots....planted and left alone all spring, summer, and fall. No hilling or covering with soil. But both could be great candidates for potato towers.
Tom Wagner