Some interesting things happen when the 2D and 3D versions are extended to infinity (keeping the overall sizes the same): the surface area of the 2D reduces by 1/4 each iteration, eventually approaching zero. Similarly, the volume of the 3D version reduces to approach zero, but at the same time, the surface area of the Sierpinski tetrahedron stays constant. In other words, it becomes a solid object with a measurable surface area but with no volume!
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