Polyhedra - Hinged Nets and Snap Tiles

by mathgrrl, published

Polyhedra - Hinged Nets and Snap Tiles by mathgrrl Nov 18, 2013


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UPDATE: The modular snap-tiles in this model have now been updated to a more consistent Customizer design where you can modify size, number of snaps, and tolerances; see http://www.thingiverse.com/thing:208591.

This entry for the Makerbot Academy Math Manipulative Challenge is a set of eight hinged polyhedral nets and five types of modular snap tiles for assembling various types of polyhedra.

These models were all specifically built for and tested on the MakerBot Replicator 2. We stayed up late at night testing, resizing, and retesting all the hinges and snaps so that teachers won't have to! Each hinged net and snap tile is made to print as easily and quickly as possible at .3mm/Low resolution with the standard MakerWare settings, without raft or supports. The hinged nets print all on one piece, fully assembled and ready to fold up. The snap tiles print as individual pieces that are all compatible with each other.

Educational Value:
Paper models of polyhedra and polyhedral nets are a standard part of the K-12 curriculum and college level teacher-prep courses. The hinged nets included here are sturdy and easy for students to assemble and collapse over and over without the need for tape or other connectors. The individual snap tiles allow students to explore more exotic polyhedra and make it possible for teachers to construct more complicated models for the classroom.

We created each of these models at www.tinkercad.com and have made those Tinkercad files public so that teachers and students can get creative - editing, remixing, or extending as needed. If you want tighter/looser snaps or hinges, alternate side snap configurations, or different polyhedral nets, you can easily pick apart and reassemble or resize in Tinkercad, even if you don't have much prior experience with 3D modeling.

This set of models includes hinged nets for all five Platonic solids:

  • Tetrahedron
  • Cube
  • Octahedron
  • Dodecahedron
  • Icosahedron

As well as hinged nets for these other polyhedra:

  • Square Pyramid
  • Hexagonal Prism
  • Rectangular Rhombohedron

The downloadable files also include models of individual snap tiles for semi-regular and other combination polyhedra:

  • Triangle tiles with snaps in 223, 332, 222, and 333 configurations
  • Square tiles with snaps in 2323 and 2233 configurations
  • Pentagon tiles with snaps in 23233 and 32322 configurations
  • Hexagon tiles with snaps in 232323, 233233, and 322322 configurations

Mix and match snap tiles as you like or follow these suggestions for the pictured modular polyhedra:

  • Cuboctahedron - 6 of the 2323 squares, 2 of the 222 triangles, and 6 of the 332 triangles
  • Truncated Octahedron - 6 of the 2323 squares and 8 of the 232323 hexagons
  • Stellated Octahedraon - 12 of the 223 triangles and 12 of the 332 triangles
  • Icosidodecaheron - 20 of the 332 triangles and 12 of the 32322 pentagons

Or, make a 3D-printed soccer ball or even larger Buckyballs using the pentagon and hexagon snap tiles! For a standard soccer ball we suggest this print job:

  • Truncated icosahedron - 6 of the 23233 pentagons and 6 of the 32322 pentagons, plus 12 of the 232323 hexagons, 4 of the 233233 hexagons, and 4 of the 322322 hexagons

Two assembly videos:

Read more on MakerHome, Days 80-90:


MakerWare .3mm/low with standard settings.

If you want to modify any model just grab an editable copy at Tinkercad: https://tinkercad.com/users/c4Y857uk4FJ-6d-lab .


Twitter: twitter.com/mathgrrl
Hacktastic blog: www.mathgrrl.com/hacktastic
Shapeways geekhaus store: www.shapeways.com/shops/mathgrrl

This design and all associated pictures and files are licensed under the Creative Commons Attribution Non-Commercial Share Alike license. If you want to use designs, images, or files outside of the terms of this license, please email [email protected].

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Matgrrl, your work is awesome and inspiring.
I've been working with designs taking polyhedra as a point of departure, and how to print them flat. Your post enlighted me a lot. I would like to apply live hinges / compliant mechanisms to my designs but before experimenting with classic mechanics. This is one of the designs I`d like to work on. Im asking you for permission to use your hinge design into my polyhedra derivated designs.
Thank you!

That's a beautiful design in your picture. Thank you for asking and yes, you can use the hinges from this model. I also have a standalone customizable hinge here that you can use if you like: https://www.thingiverse.com/thing:436737

Customizable Hinge

I would like permission to share a link to this project and physical examples at my 3D Printing in the Math Classroom presentation at the Virginia Council of Teachers of Mathematics conference. Thank you. -Josh

Permission hereby granted for DesignMakeTeach to use any of my projects, photos, or printed examples at any event ever because he is awesome.

This is an awesome design! From looking at your pictures, it seems like you need multiple models for each polygon (because the sides with 2 and 3 teeth can be distributed differently). It is possible to do this with 3 teeth on each side instead (and moreover with each side identical). The big advantage is having only one model per polygon. To see an example, do a google image search for "zaks". The idea is that each side should have trough, peak, trough, peak, trough, peak (with the alternation continuing as one goes around). Joining polygons, which are part of an orientable surface, will always work as if by magic.

Very true, and very timely of you to say so, since this afternoon I *just( finished printing a whole set of things just like that... will be posted soon and linked to here. Same snaps on every face and as long as you don't try to make a Mobius band or Klein bottle you'll be fine, as you point out! The new ones are also designed in OpenSCAD so you'll be able to customize the gaps and tolerance level of the snaps.