The Fitful Flog

March 15, 2008

Projective Planes Drifter

Fujimoto Cube with 16-gon Iris Closure

Cue the Ennio Morricone.

Susan Goldstine came to College this week and gave a talk on topology, so I cut out of work early and attended. (Susan is no slouch of a folder, herself, by the bye — she’s done a lot of nice modular work.) Topology, I understand in dribs and drabs and some days better than others. This most excellent talk was illustrated with Lewis Carroll (always one of my faves) and crafty props and it got me thinking, backwards and forwards, as I am wont to do in the wee hours when I can’t sleep.

I know I’ve said before that Compass Rose Jars are totally tubular — that is, the eastern and western edges are butted up against each other for their entire length, as are the northern and southern edges, albeit with a fractional offset. This is also, Susan told us, a definition of a torus. (I knew that, but it’s never a bad thing to hear from someone who actually studies these things.) A Fujimoto cube is also like this — it’s a tubey cube and a cubey tube. To use the symbols she used:

Fujimoto Cube Schematic

A torus can be colored like a map, but you need seven colors. (You’d think Dunkin’ Doughnuts would get on this idea, but not so far.) I figure, why not liberate an SVG from Wikipedia, warp it a little, and fold an illustration? I use my favorite iris closure, here, so you can see inside and groove on the continuity of color. Neatocooloweizenheimer!

Here’s a map with a ghost crease pattern on it. (Postscript for the PDF-deficient).

Fujimoto Cube with 16-gon Iris Closure

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3 Responses to “Projective Planes Drifter”

  1. 1
    Tom Hull Says:

    Hey hey! My main squeeze sarah-marie was at that talk too. (She and Susan are pals through the mathematical fiber arts scene.)

    Very cool torus-coloring fold! I can’t quite see what you’re doing on the bottom of it, though.

  2. 2
    oschene Says:

    Yes, I thought I saw some teal tresses, but I didn’t get a chance to say hello — had to catch a bus.

    The bottom is where the layers swap:
    Fujimoto Cube with 16-gon Iris Closure

  3. 3
    Mélisande* Says:

    About torus, have you ever seen the comic on Polly’s website ?
    (Link is at bottom right)

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