One way to view the 5s on an icosahedron is to look instead at a dodecahedron. If you connect the centers of each of the triangles in an icosahedron, you get a dodecahedron. Now connect the centers of each of the pentagons on the dodecahedron, and you have an icosahedron. Pretty cool.
By the way, for years I've had plans to eventually build a greenhouse shaped like an icosahedron with 5 of the triangles removed (it sits on the resulting pentagon). I suppose I'll still do it one of these days, but I have other priorities for my money first.
You have plenty of time left. Why not clean off your piece of glass and do a reshoot to lose the fingerprints?
-- Victor
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29-Aug-2006 05:51
Thanks for the comments, y'all. I've had this piece of glass for years and just now see a fingerprint on one of the [reflected] faces, ha! Its sitting on the background of my wife's Yoga mat in my sunny front yard. There ARE a lot of fives in an icosahedron.
Here's one of those puzzles...how many 5's are there? Counting edges, vertices, equilateral triangles and groups of these, huh? Oh, geez, and what about reflections? "B^D
Anyway, icosas are my favorite geometric figures. I've built several geodesic domes and even designed my own home using a four frequency version of this famous Buckminster Fuller promoted structure. That's the kind of a weird guy I am. Many viruses are 'built' on this shape, having as few as three molecules of protein per triangle. That's some super-macro. Thanks again, -mikey
