Tetrix

This 3-d analogue of the Sierpinski triangle forms the School of Maths Christmas tree. It's the tetrahedral equivalent of the Menger sponge but, because tetrahedra are minimal solids [you can't have fewer faces] much more of the solid is removed as the fractal is created. So, you end up with a diaphanous, delicate and, I have to admit, rather attractive object, rather than the Menger sponge which I find to be a somewhat oppressive and granitic block.

The Tetrix is mathematically more elegant, too, since the surface area remains constant as each level of the fractal is constructed, whereas the enclosed volume is halved. Thus the limiting volume is zero and the limiting surface area is constant.