Reuleaux Triangle 3D
A surface of constant width has the same height and width no matter how it is oriented. A sphere is not the only 3D surface with this property.
Notice that the surface touches all four sides of the enclosing box, no matter how it rotates.
The surface shown here formed is a surface of revolution of a Reuleaux triangle -- rotated about the line passing through a vertex and the midpoint of the opposing side.
References: Surface of constant width, Reuleaux triangle, Reuleaux tetrahedron
Click Roll to see the object spin around inside the box. Observe that the box always lies tangent to the sides of the object.
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