The first tetrahedral 3D prints

meshagon collection

A collection of meshagons

When I wrote about Dizingof’s tetrahedral meshes, a Todd Doehring, Ph.D. commented to inform me that he was the first to produce 3D printed tetrahedral models, what he calls meshagons. I love those types of comments because they end up in me learning so much, so I got in touch with Todd.

3DP: This method of model generation is very intriguing. Tell me about your program.

TD: The main tetrahedral mesh generation program was written by me over the last 10 years or more. It is called VolMesh. It is based on the work of Olaf Persson’s ‘Distmesh’ program. I did this for bioengineering analysis and also for teaching in class (and also because I’m obsessed with meshing). The idea is to take a volumetric image, either from MRI/CT, or from a generated/drawn object, and automatically convert it to a high quality tetrahedral mesh.”

meshagon cube

3DP: And then it’s ready to print?

TD: This is the base mesh generator for the Meshagon project, but I had to make several changes to generate the Meshagons suitable for printing. One big change was to remove ‘slivers’ or thin tetrahedra, which are not suitable for 3-D printing. Slivers are hard to remove, especially for complex objects. This took a lot of work.

meshagon omega

3DP: And then it’s ready to print?

TD: After I achieved suitable wireframe meshes, the next step was to try and convert them to printable objects. First, I tried ‘skinning’ in Blender3D but it would not work. Skinning cannot achieve manifold for complex joints/objects. This turned out a lot more difficult than I thought it would be. I’ve been working on it for almost a year now.

3DP: You clearly got it to work very well. What are your plans for the software?

TD: I’m definitely going to have a crowdfunding for the meshagons. I’ll be offering ‘intro’ perks like a choice of small intro 2″ meshagon sculptures, 6″ medium size, and 12″ large size. Ultimate perks could be custom meshagon sculptures. I will work directly/personally with the contributor to make whatever they want (given some parameters). The main goal of the campaign will be to fund software development to enable release of a software system. There’s a lot of work that needs to be done… code needs to be ported from Octave, GUI, etc. Another possibly easier possibility would be a Blender3D plugin.

meshagon egg

I would love for it to become a Blender plugin because it already has 3D printing tools built in. Todd is also working on a skin for the meshes, which is necessary for engineering components, and really anything that’s going to be handled and used. There are many applications for such models, from biomedical to architectural. “Since meshagons are directly developed using a Finite Element method, analysis of part strength and integration with larger systems can be accurately done. Ultimately, meshagons can be parametrically adapted to optimize strength while minimizing part weight.” 3D printing already boasts high strength/weight ratios, and this technology will improve it even further. If you’d like to read more about Todd’s process, check out his website.

  • greg crowe

    make those full sized and the kids would have a ball in them

  • bonooobong

    It’s always funny when these designer’s are claiming they’ve developed these algorithms… Dizingof has copied some works of an other israeli Shapeways artist, and I’m sure that Todd Doehring isn’t the owner of the right for that mesh tessellation algorithm. Btw, he doesn’t need to create a plugin in Blender, because it is already available as a grasshopper definition (also freeware), just check out what you can make with Weaverbird and Lunchbox plugins in GH, there are some really cool components. You also can check my works, I already 3d printed some of Dizingof’s designs as well, and I have designed a lot of math art stuff as well. And a fact is a fact: geometric rules, forms or algorithms cannot be copyrighted. AN other question would be: what if I would remodel a Dizingof sculpture? Who owns the rights?

  • Dizingof


    Somehow i always knew you have issues with original designers.. You are 3d printing my designs almost on a weekly basis to get free reputation – Your website is full of my designs..
    If i hadn’t forced you to put attribution to the original designer you’d claim my designs as yours..

    Do the community a big favor don’t piggyback on someone else work – design some of your own !

    As for claiming i “invented” this algorithm – i didn’t.. did.. to which i tweeted:

    I’ve used 2 methods to create this design technique one thru a $7k software demo and now with a free open source software.

    As for which technique is more flexible, decide for your self – I can use this technique on any organic object not just on low poly geometric shapes.

    Here is how to do it in a nutshell:

    1. Load your design into the free open source Wings3D – Select the model – Right click menu – Lots More – Tetrahedral Substitution
    2. Select all edges – Right click menu – Tubes.

    That’s it.


    • bonooobong

      It’s okay, i’m not a hater, I just wanted to clearify that an algorithm (described above) cannot be copyrighted.
      And I don’t have any issues with designers (i am an architect/designer as well) don’t get me wrong, and I don’t wanna make the trouble, AND I linked to your url (former thingiverse, now ponoko site) every time I published a photo from 3d printed objects featuring your designs. I also have my own stuff on several pages including my 3d printer blog.
      But some of them haven’t been yours, and that’s why I feel glad about your quick reply here: I’ve done a really similar paneling to a Klein-bottle like you did in one of your designs (of course I can mail you the grasshopper definition if you want) and I guess you’ve thought it is a scaled version of yours and you wanted me to give credit to you, and that’s why I left my comment here: because you cannot own neither a surface/mesh tesselation technique nor a form like the klein-bottle, and these ‘usual’ design tools can look really similar..

  • Dizingof


    The fact that you can successfully paint the “Mona Lisa” doesn’t make you Da Vinci..

    Be original, Be unique, Be happy.

    Good luck.

    • geeklove3d

      Sais the designer who copied his brand from an existing brand.
      (Dizingof is a well known design brand outside of the 3d-printnerd circle)

      You have been copying other work, for years, and you still claim it as your owe.
      And you do not even hint at who your inspiraton was.

      Gyrod with holes, did you think that up yourself?
      Or copied from the very popular Batsheba work?

      A klien bottle with holes, come up with that yurself?
      No, bathsheba did.

      And you even tried to pas her work off as your own.

      How about the reaction diffusion stuff?
      Nervous System introduced it to 3d printing.

      meshlab tutorials no doubt. stuff is older than shit.

      And most of your other work is copied from lesser know artists.

      When caught, you claim “it’s math”, but god forbid others should make something that look like your work,
      than suddenly everyone is bad, but you.

      And now you claim others should be original..
      You are quite laughable..


  • Dizingof


    There are no more free Dizingof designs to download from Thingiverse..
    You can buy my designs here: