The Dodecahedron Fractal

The dodecahedron has 20 vertices and 12 faces, all pentagons. The dodecahedron fractal grows in powers of 20, meaning that 20 dodecahedra can be put together in such a way to form another dodecahedron, with volume removed.

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This is a stage-1 dodecahedron fractal set inside of a dodecahedron, made from transparency film. Yingxian Zhu made the patterns and colored them, keeping the tabs clear so not to have color on color. The patterns (20 interior dodecahedra and 1 outer dodecahedron) were spliced using an exacto knife. The best way to put these together at the tabs (that I have found when using transparency film) is to use a very thin double-stick tape. That wasn't used here, I tried using glue instead, and the edges are a mess.

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This, also, is a stage-1 dodecahedron fractal, made much earlier, and it is VERY small. The interior dodecahedra are tiny, about 7mm edge-length, no kidding. It is made from transparency film, because I wanted it to be clear, but you will notice that the interior dodecahedra are difficult to see, there is little visible definition, which is why the structure in the row above was made with colored dodecahedra. Problem was (with the structure in the first row), the interior dodecahedra weren't transparent, the color made them opaque. If anyone tries this themselves, in order to add color yet maintain a fairly transparent structure, you might try adding color to the patterns in semi-transparent form. That way only half the pixcels will have color on them. I haven't tried this, but I suspect it might give decent results.

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Above is a still image from a Quicktime Movie made by Reimund Albers showing transition stages in growth in the dodecahedron fractal. Practice trying to see the outer dodecahedron shape that is maintained while volume is being removed. As the volume approaches zero, the outline of a dodecahedron, thready though it might be, will always be maintained.

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