Sierpinski tetrahedron
By George Hart for the Museum of Mathematics
A classic 3D fractal is the Sierpinski tetrahedron, which is a tetrahedron of tetrahedra of tetrahedra, etc. This fifth-order model is about 8.5 inches along its edges. It is made from nylon by selective laser sintering. If you have access to additive fabrication machines, you can make your own copy of it using the STL file available here.
The Sierpinski tetrahedron is so elegant that it has inspired many people to construct it in many materials. Alexander Graham Bell made giant kites with wood frames in this form. I love this geekly romantic photo of him kissing his wife in one.
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