The Icosahedron Fractal

The icosahedron fractal grows in powers of 12, corresponding to the number of vertices of an icosahedron. This means twelve icosahedra can be constructed to form yet another icosahedron, with volume removed.

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Above is my one and only experience in making an icosahedron fractal. I made it for my granddaughter, Sydney Renee, then 20-months old, in March 2005. Now she is almost two. She likes it, and of course has no idea what it is, nor do I try to tell her. We throw it across the room and have fun with it. Her eyes can see the pretty patterns, and as she grows up, she will be able to learn more about it and appreciate it in different ways.

It is rather subtle, but try to see the outer icosahedron shape made by these 12 icosahedra set tip-to-tip.

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This is one of Reimund Albers images of a Stage-2 icosahedron fractal taken from his Quicktime Movie that shows two stages of growth. Next to it is an image of a hand-made Stage-2 icosahedron fractal.

In Reimund's computer-generated image on the left, it is easy to see the 12 Stage-1 icosahedron fractals, since they are each shown in a different color. Perhaps this can be used to help identify the 12 Stage-1's in the image on the right, made by participants under Reimund's direction at Peitgen and Voss' 2001 Florida summer institute.

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These are images from a geometry institute in Munich,(the LMU Mathematishches Institut's Geometrie-Wochenende 19.-21. Jan 2001 an der Universitat Muenchen in Zusammenarbeit mit "Spektrum der Wissenschaft") that Reimund attended in January 2001. The photos were taken by Reinhard Weber. The left image shows twelve completed stage-2 icosahedron fractals waiting to be connected into a stage-3 icosahedron fractal. It is nice that they are laid out this way, so you can actually count them. In the image on the right, the stage-3 is about half-built, giving an interior view of what is to come.

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The completed Stage-3 Icosahedron fractal built at the Munich workshop referenced above. Can you see the Stage-2's within the structure? See other photos from their workshop here.

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