Thursday, December 3, 2015

Perfection with 14 Sides

Truncated octahedron From en.wiki made by user Cyp using POV-Ray
One of the primary advantages of additive manufacturing is the ability to build structures that would be impossible to create using traditional subtractive machining. This can be particularly important for aerospace and automotive applications where reducing weight while maintaining structural integrity can generate substantial fuel savings.

Weight reductions can be accomplished by using titanium and other lightweight materials which are easier to print than machine. It can also be accomplished by replacing solid structures with partially hollow structures.  The key is removing as much material as possible without compromising the strength of the part.

To create the internal shape of a strong, lightweight part, a truncated octahedron may be the world's most perfect shape. A fourteen sided polyhedron composed of six square faces and eight hexagonal faces, a truncated octahedron has edges which are all the same length. A truncated octahedron can be created by joining two square pyramids at their based then cutting off all six of the corners to remove one third of the edge length.

Truncated octahedra.jpg by AndrewKepert.
One remarkable feature of truncated octahedra is they stack together to completely fill a three dimensional space without any voids. An object constructed of hollow truncated octahedra is lightweight and strong enough to resist shearing and buckling. The strength and weight can be varied within a single part by varying the thickness of the walls or the size and quantity of the octahedra.

What is your favorite shape?

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