A Polyhedral Journey

So I wondered, what would happen if I took rhombic dodecahedra…

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…and then affixed them to the sixty wider faces of a rhombic enneacontahedron?

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Well, it turns out that this is what you get:

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It’s at time like these — urgent situations in recreational mathematics — that I am most glad I bought Stella 4d, the program with which I made these images (and which you can try, for free, at http://www.software3d.com/stella.php). This would have taken months to figure out without the proper software! The next thing that occurred to me was to take the convex hull of the last polyhedron. That’s like draping a sheet around it and then pulling it tight. Here’s the result:

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Stella owes its name, in part, to a complex operation involving extensions of edges into lines, or faces into planes, called stellation. Stellating the above figure gave me something I didn’t like, but stellating it again gave me this:

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And then, after six more stellations, I arrived at the end of this particular polyhedral journey.

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On Loving Christmas But Hating Xmas

I may have heard the objection a thousand times, living here in Arkansas:  “They’re trying to ‘X’ out the ‘Christ’ from ‘Christmas!'”

Such people have apparently never heard of one of the most ancient Christian symbols in existence (and still in heavy use):

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Chi and rho are the first two letters one uses to spell “Christ” in Greek, the original language of most of the New Testament. It makes much more sense to interpret the “X” in “Xmas” as a reference to Christ, through the “chi” in the “Chi Rho” symbol, rather than some insidious plot to eliminate Christ from this holiday — a holiday with a history that, as many people know, predates Christ by centuries, anyway.

Of course, those people who object to “Xmas” don’t know about the Greek letter chi, or the fact that it looks just like an “X,” as used in English, or that the two letters represent very different sounds. There’s no shame in simple ignorance, curable as it is by education. However, I would wager that most of those who object to “Xmas” also do not want to know these things, either, and in that, there is shame. Not wanting one’s own ignorance to be replaced by knowledge is an excellent definition for stupidity.