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update : a revised script and set which includes 4,5 and 6-fold vertices ( slash facets, not sure which to call these ) can be found at http://www.thingiverse.com/thing:4934 and http://www.thingiverse.com/thing:5028.
These two triangular pieces can be assembled into any polyhedron based on equilateral triangles. This includes tetrahedra, octahedra, icosahedra, and many others.
The structure of the pieces is such that they resemble both faces and vertices, so the octahedron is also cube-like, and the icosahedron also looks like a dodecahedron. ( a tetrahedron is self-dual, so that doesn't count ).
Print out two each of Y1 and Y2, assemble into tetrahedron
Print out four each of Y1 and Y2, assemble into octahedron
Print out ten each of Y1 and Y2, assemble into icosahedron
A range of other shapes are possible. I believe the C60 buckyball is possible with these elements.
Snap-together polyhedron verticies by mrule is licensed under the Creative Commons - Attribution - Share Alike license.
So what's this mean?
We're sure mrule would love to see what you've printed - take a photo and share it on Thingiverse as a Make.
To post a Make simply visit this Thing again and click I Made One to start uploading your photo. You can also download the Thingiverse Mobile app (available via Google Play and Apple App Store) to take a photo and upload your Make right from the app!