The Reuleaux Tetrahedron
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.
Drag the Reuleaux tetrahedron with the mouse to rotate it. Select the checkboxes to choose from the different viewing options.
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