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Solids of Constant Width (Set of 3)

from The STEMcell Science Shop

Regular price $11.95

These 3D-printed solids of constant width behave like spheres. You can demonstrate this property by setting a flat object, like a book, on them and they'll roll smoothly as if the object were on spheres. The upside is that these wonky shapes won't roll away.

The precise shape is an orbiform based on the revolution of a Reuleaux triangle. Details on that below.

Size: 30mm (1.18 in) 
Color: White
Sold in sets of 3

 

More info (from Wikipedia):

The Reuleaux tetrahedron is the intersection of four balls of radius s centered at the verticesof a regular tetrahedron with side length s. The spherical surface of the ball centered on each vertex passes through the other three vertices, which also form vertices of the Reuleaux tetrahedron. Thus the center of each ball is on the surfaces of the other three balls. The Reuleaux tetrahedron has the same face structure as a regular tetrahedron, but with curved faces: four vertices, and four curved faces, connected by six circular-arc edges.

This shape is defined and named by analogy to the Reuleaux triangle, a two-dimensional curve of constant width; both shapes are named after Franz Reuleaux, a 19th-century German engineer who did pioneering work on ways that machines translate one type of motion into another. One can find repeated claims in the mathematical literature that the Reuleaux tetrahedron is analogously a surface of constant width, but it is not true: the two midpoints of opposite edge arcs are separated by a larger distance.

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