The Fitful Flog

November 20, 2005

Pentagonal Compass Rose Box and φ-Quiddity

Pentagonal Compass Rose Box

Howdy — coming here from the Origami Resource Center? Welcome, but please be advised that this particular model is crazy difficult and just about anything else on the site would be easier to fold. Here, try the model menu.

This is the Pentagonal Compass Rose Box, made from a golden rectangle.

CP for American letter paper

CP for A4

The CP is meant to be white side up; blue is mountain fold, red is valley fold.

This model comes out of a lot of thought about current origami chatter and the nature of things. I have been turning over an idea in my mind about an open-source origami rose – folders love those complex roses, sometimes with an inordinate love. I was thinking that we should have a new line of roses, somehow distinct from the Kawasaki line and entirely open to variation without propertarian hoo-ha.

It’s one thing to consider this a desirable object, quite another to invent it.

And then, I wanted to avoid the tyranny of 45° and 22½° angles and even the insurgent purity of 30° and 60° angles. No, I thought, the open-source rose requires ?-quiddity to make it go, for only five-fold symmetry will make it come alive.

Well, I’m not there yet. The open-source rose remains one of those ideas that rotate in front of me when I’m drowsing between the snooze alarms. But there’s always the creations on the by-way.

A pentagonal compass rose box is a theoretically impossible thing. But since the theory is largely of my own making, I decided to be reasonable about it. When you twist shut a tube with an odd number of sides, the corners and sides never line up. And you can’t collapse something that doesn’t line up. But, I thought, what if you twisted it twice and bashed in the corners?

Yup, that works, though it’s not the easiest collapse I’ve seen. You get to make two collapses at once and the paper puts up a fight. Persevere. It would probably make a nice wrapping for a Christmas present.

The golden rectangle has a ratio of 1:(?5+1)/2 and is full of lovely 3-and-5 resonances. For instance, if you divide it in sixths one way, it divides itself in fifths of its own accord. and 36°, 54° and 72° angles are to be had without too much struggle. Joseph Wu has a piece on folding silver and golden rectangles here. I got a lot of the math for this from Kasahara’s Origami for the Connoisseur and Amazing Origami.

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The Pentagonal Compass Rose Box (both A4 and American Letter versions) are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

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10 Responses to “Pentagonal Compass Rose Box and φ-Quiddity”

  1. 1
    Jane Says:

    Man, that one was hard to fold! The way it closes is very clever. A had a good time trying to figure it out.

  2. 2
    oschene Says:

    Jane, I agree with you: it is absurdly hard to collapse this. This weekend, I redesigned the model to be folded from a square and to collapse in a more civilized way.

    It uses the same grid as the star-vase. Instead of two full twists in one direction (as above), I used two half-twists in opposite directions. You end up with the corners of the tube aligned and five inside reverse folds. This uses less paper, but is a little tricky to initiate. I’ll have to do it a few more times before I can attempt a CP.

    I’ve got to say, it’s impressive how you can decipher these cryptic CPs so well.

  3. 3
    Jane Says:

    I guess that’s because I’m good at following orders. When I was growing up, my brother would disassemble stuff and I’d assemble them back together – most of the time they worked too.

    Doing your origami is a bit like both – I have “instructions” (you do leave a lot of clues on your entries) and I have to put things together so it works.

    A friend of mine saw the photo of the one I did and when he found out it’s made from a golden rectangle, he said he had to do it (he’s a math professor).

  4. 4
    blast Says:

    com? q faiz tio????

  5. 5
    oschene Says:

    Hey, blast!

    When someone speaks Portugese to me, I either feed it through Google (which unfortunately uses a Martian dialect of English) or ask my friend, Rosa, who grew up in Portugal and gives me recipes for febras. This time, though, I’m going to rely on eight weeks of accelerated Latin and guess you’re asking, “How the hell do you do this?” Or you’re insulting my uncle.

    Okay, it’s not easy and it defies conventional and uncoventional diagramming. Jane (who does speak Portugese, by the way) succeeded in folding it, I’m not sure how. If you look at the Star Vase diagrams, you’ll see a single twist of a pentagonal tube offsets the bottom half. However, it you twist it twice, you line the halves up again. It leaves corners sticking out that need to be folded in. It’s not wicked easy to collapse.

    In many ways, this was a transitional piece and I hope to publish more transparent variations of this soon.

  6. 6
    nelson Says:

    What does that means – golden rectangle? Please, help me.

  7. 7
    oschene Says:

    It’s a rectangle with special properties: try here

  8. 8
    May Says:

    Found this website a couple of days ago. Never saw a CP before then, and I made it my goal to solve this one. I can now say Mission Accomplished 🙂
    Very challenging, I spent many hours trying to figure out how to make the double collapse in the middle, and then the edges weren’t even so the top collapse wouldn’t work. Worth every minute of puzzling, gorgeous creation. Thanks!

  9. 9
    Jordan Says:

    We’re are the instructions

  10. 10
    oschene Says:

    No, you’re not.

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