Main Concept

What object, when placed under a flat plate on a smooth surface, will allow the plate to roll without* wobbling? The Reuleaux tetrahedron, due to its almost constant width, is an example of this type of object. The Reuleaux tetrahedron is the three-dimensional intersection of four spheres of radius $s$ centered at the vertices of a regular tetrahedron with side-length $s$. A sphere centered at any one of the vertices has the other three vertices on its surface. *Note: The greatest width, measured between two opposite edges, is approximately 1.02 times larger than the smallest width, which is measured between a vertex and its opposite edge. This difference will only lead to minimal changes in the plate's height as it is moved. The movement will be relatively smooth.

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