I call it the 3 – 4 – 5

Because it has squares for sides that meet with three or five in the corners.

Meet my new crocheting project, a regular twelve-sided polyhedron in disguise…

haaksel open

As you can see, it’s open on one side: five squares are missing.haaksel_bakje

The advantage of this missing part is that you can turn the whole thing inside-out, like here. In this picture you can clearly see a five-corner and a three-corner. The yarn I used changes color every 30 cm or so, giving these nice stripes.

How is this a dodecahedron you ask?

haaksel_met_lijnen
Well, take a corner where five squares meet, and draw a pentagon around it. It consists of five triangles, each one-half of a square. You can do that on every ‘five-corner’ of the bowl (including the one that’s not there), none of the pentagons will overlap, and there are twelve of them.

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  1. Machiel

    Leuk, zo’n aaibaar wiskundig figuur! (Ff in het Nederlands, want het Engelse equivalent van ‘aaibaar’ wil me niet te binnen schieten, of toch, ‘strokable’?)

  2. This is amazing. I love it!

  3. Dank je / Thanks!

    • Carol Ann

      I love the 3-4-5! I have been searching for a pattern for a twelve sided die for a friend who is a long time player of games. I would very much like to have the pattern for my own use (not to make to sell).

      Would you be willing to share the pattern? I would be happy to purchase the pattern.

      Thank you.
      Carol Ann

  4. Wilfred

    Can we now expect all the platonic solids? Can we do requests?

  5. Well, at the moment I’m more into the variations on platonic solids (as this one is), but of course you can do requests! (although I don’t promise anything…)

  6. Wilfred

    Well, if you can pull it off an icosahedron would be cool.
    A Torus perhaps?

  7. Icosahedron is easy – take this thing here, and look at the triangles (where three squares meet) as the sides. Such a triangle consists of three halves of squares and there are, or would be if it was complete, twenty of them. Ta dah!

    And I’ve done a torus before, too.

    Anything else? :-)

  8. Wilfred

    Well, there is also a double torus, and a triple, and a … :-P

  9. Hm, help me here, what’s a double torus?

    My latest project is based on the picture found here

  10. Wilfred

    See: http://en.wikipedia.org/wiki/Double_torus
    You can add as many holes as you like. :-)

  11. Oh, of course… that’s a good idea!

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  14. Wendy

    How did you make the different faces? Are they continual, made in one piece, or sewn together?
    And,
    Have you seen Miyuki Kawamura’s squeletons of platonic solids? Would you know how to make them? I do not have the mathematical knowledge for that, but I’d love to be able to make some of the models in http://www.toroidalsnark.net/mkexh2005/mkexh2005-Pages/Image5.html
    All the best!
    Wendy

  15. Hi Wendy, thanks for the opictures of the ‘skeletons of Platonic solids’. I hadn’t seen it before, it looks pretty cool!

    As for your first question: the faces are crocheted one after another, every time using the side of a ompleted face as the base for the next. (I’m not sure if that’s what you mean by continuous?) I always try to make it so I don’t need to sew anything, and in this way (with a little bit of cheating at some point) I made the whole thing from a single thread.

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