The cuts can be made using a tourné knife (peeling knife or bird's beak knife), but a regular paring knife will also work.
etymology: tourner is the French verb "to turn"
The technique is most often used on firm vegetables like carrots and potatoes. The result looks neat and elegant, and the uniform shapes are better able to cook at the same rate.
On the downside, the tourné cut is time-consuming unless you're very good with a knife, and you're left with leftover vegetable bits in odd shapes. Try using the trimmings to make stock, or mashed potatoes.
Tourné-cut vegetables look like tiny (American) footballs. So if your game-day snacks include root vegetables, here's a way to get creative. Or, you can impress the in-laws by bringing fancy-looking candied yams to the holiday dinner.
(Don't worry: your tourné-cut vegetables will look nice even if they have nine sides.)