THE ULTIMATE SOLID OF CONSTANT WIDTH
The ultimate expression of the Reuleaux shape creates the most sophisticated shape with a constant width.
Few surfaces keep their width while rotating on any axis; we're used to seeing this characteristic in spheres. But as incredible as it may sound, other shapes with the same property aren't circular, such as The Solid of Constant Width.
Leonhard Euler discovered that the Reuleaux triangle always maintains the same width. Four spheres with equal radii, placed at the corners of a regular tetrahedron, form a three-dimensional version of the Reuleaux triangle but without the constant width. Then, Dan Bergerud replaced the tetrahedron's edges with a group of spheres touching the edges, creating a solid object with similar symmetry and constant width, the Ultimate Solid of Constant Width.
What is so special about the Ultimate Solid of Constant Width?
In the mathematician world, it is known as Spheroform
It is the only three-dimensional shape that combines constant width and Tetrahedral Symmetry.
It conveys the knowledge of one century of discovers and mathematical analysis to find the right equation that creates this shape,
“This paradoxical solid stems from studies made from the 18th century to our days.”
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