Mathematicians find odd shapes that roll like a wheel in any dimension

A 3D shape of constant width as seen from three different angles. The middle view resembles a 2D Reuleaux triangle

Andriy Prymak et al. 2024/SageMath/Danylo Radchenko

Mathematicians have reinvented the wheel with the discovery of shapes that can roll smoothly when sandwiched between two surfaces, even in four, five or any higher number of spatial dimensions. The finding answers a question that researchers have been puzzling over for decades.

Such objects are known as shapes of constant width, and the most familiar in two and three dimensions are the circle and the sphere. These aren’t the only such shapes, however.…

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