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Sunday, May 8th, 2005

Time Event
12:54p
Family resemblances
Apparently someone leaked a photo of my little sister and myself a few years ago.

Seriously, the conversation this illustrates probably happened. I remember part of the previous dimension's version clearly; it went something like this:

Robin: And what shape is it?
Wendy: (smiling proudly) A hessagon!

And since the dodecahedron is one of my favorite polyhedra I undoubtedly discussed it with her as well, though perhaps not at the same time. I don't remember when I got so into all this stuff, though I'm sure that interest in Escher was the catalyst. Probably around ten years ago, maybe more. I do vaguely recall looking carefully at the shape of the garnets we got at Wrangell, AK in 1992 (rhombic dodecahedra, not to be confused with the one Lisa is explaining) so perhaps it was as far back as then.

The roots were surely earlier, though. My dad's collected pyrite cubes for years, though not so much recently -- the first he bought is still probably the best. He just thought it was really interesting that a mineral grows in such a shape. That principle stuck with me, though it didn't always occur to other people, who would give him amorphous pyrite, missing the point. And Mom has always enjoyed Escher's work; for as long as I can remember there's been a poster advertising a showing of his stuff at San Francisco's Vorpal Gallery in 1972 pinned onto a door in the house. And in an effort to cover up the unbelievably ugly wallpaper in the house's single bedroom she put pictures she liked over it, including several copies of Escher prints; when the bedroom became mine (later Wendy's) following the addition of a second story I kept the pictures and would stare at the Metamorphosis (II) going across the top, or the two hands drawing each other, trying to figure them out.

My sister hasn't, so far as I know, really followed this path herself...but her favorite shape is the star, and of course the elegant mathematical properties of the star (I suppose properly termed the pentagram, but I dislike the connotations of it) have been known for centuries (or millennia? when was Pythagoras?). Perhaps its golden-section proportions says something to her subconsciously. I'm sure part of the appeal of the Triforce to me is its charm as three equilateral triangles, with a fourth in the space between them...I can't help but think that the proper form in 3D would be four tetrahedra forming a large one by touching at the corners, with the middle octahedral space empty. However, Tetraforce just doesn't have the same ring, however much it might go with recent installments.

(As for the sudden segue from Wendy's stars to the Triforce, I was thinking of the multitude of glow-in-the-dark stars on her bedroom walls, when she finally got sick of the aforementioned wallpaper and painted the room. She offered to let me paint something on it and I stamped a triforce in gold in one corner, since I had been in the process of stamping them all over my boring black suitcase so I could actually find it at the airport. See, my thought processes make perfect sense.)

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