Thursday, October 13, 2011

Rhombic Dodecahedron Puzzle

I just shared a simple Rhombic Dodecahedron Puzzle at Thingiverse, consisting of four identical pieces that fit together to form a solid shape.  The concept is very similar to my previous marble puzzles and cubic trisections, but using four parts instead of just two or three.

The idea of using a shape with four-way symmetry was inspired by George Hart's Air puzzle, which is described on his web site and briefly demonstrated in a YouTube video by Roxanne Wong.

Like my previous dissection puzzles, the pieces have a distinct orientation so they only fit together if they're all pointed the same direction.  Technically that means my puzzle only one-eighth as many duplicate solutions as Air but that doesn't mean it's any harder to solve.

Here's a video that demonstrates how the puzzle works.
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5 comments:

  1. WizarthOctober 14, 2011 at 3:08 AM

    How did you model this?

    ReplyDelete
  2. GeorgeOctober 17, 2011 at 6:46 AM

    Dare I suggest: Dodecahedron in 5 pieces?

    ReplyDelete
  3. Scott ElliottOctober 17, 2011 at 1:09 PM

    Wizarth, other users have asked the same thing so I will add my source data at Thingiverse. It was initially modeled in Alibre but it kept exporting defective STL meshes so I re-did it in OpenSCAD.

    George, the corners (vertices) of a Platonic dodecahedron have 3-way symmetry, not 5-way. To get 5 identical pieces a dodecahedron would have to be dissected from face-to-face. (Its dual, the icosahedron, could be dissected from vertex-to-vertex.)

    That raises an interesting observation: I've considered a face-to-face division of a solid, but never tried to build one. It's intriguing that other designers who've built similar dissections (George Hart, Oskar van Deventer, and Robert Ried) always used vertex-to-vertex or edge-to-edge schemes. Come to think of it, though, Bram's "Trapped Marble" includes a face-to-face bisection of a rectangular prism.

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    Replies
    1. Chris K. PalmerMarch 31, 2014 at 2:30 PM

      Hi Scott,

      Just saw this surface on thingiverse. I also made one of an R12 with four pieces but I ended up preferring and R12 with 2 pieces. I have done a nice cuboctohedron face to face with 3 pieces and a dodecahedron vertex to vertex with 3 pieces as well. All can be printed on my Type A Machine FDM without support or even infill (If the excellent kisslicer algorithm is used).

      George Hart wrote software (probably in java) to make any slide together with parameters some years ago. My first intro to this idea was from Rinus Roelofs.

      If you want I'll send along files. I haven't published it as I consider it not really my idea even though I did work on it and have made more than a few for friends and family and because thingiverse has disagreeable (to me) terms of service regarding content and attribution.

      Cheers,

      Chris K. Palmer

      Delete
  4. GeorgeOctober 17, 2011 at 4:46 PM

    Yeah, I was thinking of dodecahedron face to face. Or maybe, try the icosahedron?

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