## Tuesday, 25 November 2008

### Dodecahedron

I fancied making a dodecahedron, an object with twelve pentagonal faces. It is an interesting shape and, as the sides slope at ~26°C, it can be made without support material. I searched the web for a 3D model for some time but could not find one. I also searched for how to model one in CoCreate, as it wasn't immediately obvious to me. That came up blank as well so I had to figure it out myself.

I started with a construction circle and divided it into 5 sectors with construction lines 72° apart. I joined the intersections to make the base pentagon.

I then extruded that to a height equal to the circle radius and with a draft angle of -26.56505°. This is the dihedral angle (2arctan((1+√5)/2)) minus 90°. That makes the base of the object and the first line of vertices above it.

I then made a new workplane on one of the partial faces. I projected the face onto the workplane and then added a construction circle through three of the points. A vertical line from the centre gives the missing fifth vertex where it meets the circle.

I then join the vertices to make the pentagon, extrude it inwards (negative) by the circle radius with the same negative draft angle.

That operation has generated two partial faces with all five vertices. I construct the pentagons from the vertices and extrude inwards by the circle radius until the shape is complete. A total of eight extrusions are required.

I then shelled the object to 2mm to make it hollow. That created a second part inside, revealing that the construction does not in fact make a complete solid. If that was important one could extrude one of the faces more than half way through, with no draft angle. I just deleted the second part.

The finished item is about 2.5 times initial circle radius across opposite flats. This one was based on a 10mm radius circle.

The file is available on Thingiverse.

1. This totally reminded me of dungeons and dragons dice :) so taking that a step futher you could build a full set of dice AND make those little characters that cost so much from the gaming shops.

Please don't let dungeons and dragons be the 'killer app' for rapid prototyping :)

2. I know this is called rapid prototyping, but has any research been done into post-processing the objects to make them more aesthetically pleasing? ie. what can you do in the way of sanding/filling/painting extruded hdpe/abs to stop it looking like a very carefully wrapped ball of string?

3. No I don't think anybody has tried anything yet.

Ian Adkins has suggested dipping in MEK solvent would give a smooth surface. I expect Acetone would have a similar effect, but neither are very nice chemicals.

With a simple convex shape like this I could clean it up on my bench sander.

I wonder what would happen if I put it in one of those rotating drums full of sand that are used for polishing stones?

A milling pass with a ball mill after every layer would give a smoother finish.

Using 0.25mm filament also gives a better result as it starts to get below the resolution of ones eyes (mine at least).

4. Another way to get dodecahedrons and other platonic solids is to use the Platonic Solid script in Art of Illusion. The version with the current AOI doesn't work, maybe because of an API change, so I took out the crashing code and saved the updated version in the "Art of Illusion Scripts" folder in the skeinforge reprap_python_beanshell zip file.

5. Yes that works well and would have saved me some time had I known what a Platonic solid was! The original script worked with the version of AOI that I am using.

To make it hollow presumably one has to subtract two as I don't see a shell command in AOI.

Looking at the dihedral angles we should be able to print the first four platonic solids with no support and the icosahedron is only 48 degrees from vertical so might just work.