Reuleaux Tetrahedron

Geometry Level 3

The Reuleaux tetrahedron is the intersection of four balls of radius s s centered at the vertices of a regular tetrahedron with side length s s . This shape is defined and named by analogy to the Reuleaux triangle , a two-dimensional curve of constant width .

Is the Reuleaux tetrahedron a surface of constant width ?

No Yes

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1 solution

Brian Lie
Aug 30, 2018

The two midpoints of opposite edge arcs are separated by a larger distance, ( 3 2 2 ) s 1.0249 s . \left(\sqrt 3-\frac{\sqrt 2} 2\right)s\approx1.0249s.

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