Center-back moving left are a stage-2 Sierpinski tetrahedron and its Complement. In front of them sit a stage-0 and stage-1 Sierpinski tetrahedron. A stage-1 Menger sponge sits at the far-back-right of the image, in front of it is a stage-1 octahedron fractal with tetrahedra placed in the openings (because tetrahedra fit in the openings, the octahedron fractal complement is made of tetrahedra). Paul Bourke has put up a page showing all five of the Platonic Solid Fractals and their Complements, very exciting.

Each of the Platonic solids has its own fractal structure. This is a special quality about them. It means that each of them can be put together to make another such polyhedra with volume removed. You can see pictures of them by clicking on the links below or using the pulldown menu above. These are the least finished of my pages, the octahedron fractal page has no images up yet, nor does the tetrahedron fractal page, but the whole site is filled with images of the tetrahedron fractal. Dodecahedron Fractal Icosahedron Fractal Hexahedron Fractal Octahedron Fractal Tetrahedron Fractal With the exception of the hexahedron fractal (the Menger Sponge), each fractal of the Platonic solids grows in an exponential power equal to the number of vertices of its associated Platonic solid. Although the cube has eight (8) vertices, the cube fractal grows in powers of 20. There are other ways to construct the cube fractal. To be truly fractal, every part must be similar to the whole. Each of these structures will 'become' a fractal at infinity. A piece of the stage-1 Menger sponge in the above photo, for instance, is only a cube, and doesn't look like the Menger Sponge, no matter how closely you zoom in on it. The idea is that at infinity, wherever that is, every tiny piece, when zoomed in on, will look like the whole structure, and be self-similar.

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