Polyhedron Facets ( revised, parametric )

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Published on November 26, 2010
This thing was Featured on November 30, 2010

Description

This thing includes a revised parametric script for generating polygonal facets for use in polyhedra. Several possible facets have been rendered. I know that the triangular, square, and pentagonal facets presented here are sufficient for building a wide range of shapes.

Thing thingiverse.com/thing:5028 extends this set with more types of facets, including spoke-like and polygonal facets for all shapes.

I've been wanting to create a very generic snap-together set of forms for MakerBot for some time. It would be awesome to have an algorithm that generates a queue of forms to slowly grow a very large procedurally generated object.

This is a revision of things thingiverse.com/thing:4893 and thingiverse.com/thing:4899, and an attempt to create a compatible set of snap-together primitives for building geometric forms. Thing 4893 set too large a scale to print pentagonal facets. Thing 4899 had a mathematical error which caused the different faces to be incompatible. This revision corrects that error.

Instructions

Look up a polyhedron design, and print out the appropriate facets. Clean, and assemble. As long as you print out as many [+] snaps as [-] snaps, these pieces have a habit of coming together. These pieces can also be assembled into amorphous but rigid forms.

These pieces are snap-compatible with things 4893 and 4899, and shapes like the truncated tetrahedron (an octahedron with 50/50 triangles from two different scales), cuboctahedron, and icosidodecahedron, can be built by mixing triangles from one version with the appropriate polygons from another version. This creates a rigid solid that can serve as an interface for two different sets of piece sizes, if you are building some sort of amorphous structure.
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Cool, was looking for something where i could print a reasonably small thing for each spool. Was thinking of some kind of flowers with petals, but this will do better,

Anyone else having problems with the tool path generation on the newer skeinforges? I cant seem to get anything bigger than the 3 studs to generate without getting an error that kills the program.

Hi, this is great, thanks for doing it.

I have managed to print out all the pieces for the large polyhedron like the multicolored one you built.

I am having some issues with assembly though. The last piece I put into this is the largest H1 piece. Now, I have about 2 empty holes where an H1 should go but the pieces don't line up at all
. The pattern on the empty hole goes 2, 1 ,2 ,1, 2,1 where normally it should be 2,2,1,1,2,1.

On top of that, I have 5 holes where I am going to have to mirror X in order to assemble with the good side facing outward. Should I have to do this? Because originally I printed 20 H1's as they were, an
d as they are, I am going to have to put them raft side facing out, which I don't want to do.

I know you have a picture of the entire thing spread out on the floor in pretty high resolution, but
there are a lot of pieces and it is hard to see how each line up. I tried looking up polyhedrons
online, but all I can find are the triangular shaped ones that don't seem to have these connector issues.

Is there a higher resolution of the picture of it laid out flat some where else? Or some other way to figure out how to assemble this? I can't just give up as I already have a few lbs of plast
ic tied up in this print.

Thanks!

I added two more hexagon pieces that might help you, also added to the script.

If you look in the script, the notation for the snaps is much like the notation you used in the post, except 0 and 1 instead of 1 and 2. not sure which is which.

you caught me : its actually impossible to assemble the large polyhedra that use hexagons without putting a couple hexagons raft-side-out.

On my machine the raft side looks rather nice so I never thought about it.

I *think* its possible to assemble it without mirroring the squares. This is how I thought of it : imaging building a dodecahedron ( or truncated icosahedron ). The squares just space the parts out a bit without changing
the sign on the snap. So, you shouldn't need to flip them.

So, sorry about that. There is a script associated with the thing that would let you design customized hexagons. If you want to play with that it could help. But, I think I'll take a look and try to generate a couple alternative hexagons an
d post them here in a bit.

--mrule

This is really nice, especially if you have many colors (which I don't have, see green picture above). The parts snap very well together. Maybe it would be nice if you could wirite the number of part you would need for different designs. Now I checked from the picture with the pink and blue parts how many you probably used. I combined 6 "q" parts, 16 "t1" parts and 16 "t2" parts on a 12x17 cm bed and printed all parts in one go. Next time I will print it a bit larger.

Merci pour toutes ces informations

@ +

Thank you for all that information :)

Hello,

It's possible to have in DXF ?

I'd like to achieve in PMMA

Oh, but I see on your list of tools you have a laser cutter but no 3D printer, correct ? This [ http://www.thingiverse.com/thi... ] thing seems to be similar to mine, but can be made with a laser cutter.

The open source program meshlab ( http://meshlab.sourceforge.net... ) can convert .STL to .DXF, and do other fun manipulations on meshes. You should check it out.

These would be a perfect application of raftless + automated built platform.

An extension of this set of pieces would be a set of pieces for constructing a large object out of arbitrary small facets. For example, a mesh model could be refined in sufficient small triangles. A script could generate the .STL files for a snap-together version of each facet. Then, the whole thing could be printed and assembled as a puzzle. The space on the interior of the facets is flexible, so that could be used to add other features : more snaps, mounting points for hardware. Maybe we can make more of mendel fastener-free. The snaps are currently designed to rotate freely as hinges, but structural applications might require a high-friction snap ( easily adjusted in the script ).

What if you went with connector that will connect with itself. then you can connect them any way you like without having to figure out the math to get the connectors to line up.

I finally followed through and did this : http://www.thingiverse.com/thi...

That snap design is genius. It looks like it will fail if you try to mate it with its mirror image, equivalent to flipping over a 3D object. So, these snaps still have limitations. At first glance though, I imagine that they would work for all convex polyhedra.