(The full title of this Instructable is Emoji icosahedral die: the ?-20 where "?" is the poo emoji)

Step 1: Build an Icosahedral D-20

In my instructable Stellating 3D models in Inventor, I show you how to make an icosahedron with a minimal amount of math. So let's start with that! The trick there is to construct an icosahedron with 20 identical sides. Any changes you make to the side Part file gets copied to every side of the icosahedron. Start with a plain triangular face.

Step 2: A First Easy Success

Using Inventor's Insert Image function, you can add an emoji decal to your triangular part. There is some reason to think the Apple images are free to use: here's how to get emoji images for your project. (Thanks to Joseph Pred for the tip!).

Step 3: Emoji Fail!

OK, so that's great, but I can't 3d print that. What I want to do is emboss the emoji icon on the side, so that it's slightly recessed: that way I can print in one material. Fortunately, Inventor has both an Emboss function: so if we can get a two-color emoji that should be easy, right?

So I found this lovely open-source emoji font; this seemed perfect because it is both monochrome and embedded in a font so I could use Inventor's Text function to add it to a sketch for embossing.

That was a big nope. Inventor simply could not handle the emoji glyphs (on Windows, anyway), even though it did fine on other symbol fonts like Wingdings. Fail.

Step 4: Vectorizing the Poo

Another big nope: the OpenSansEmoji symbol, while perfectly respectable, lacked the big eyes and smile that I for one associate with the Pile of Poo. So back to the drawing board, in this case Inkscape, the wonderfully powerful yet delightfully open-source vector drawing program (think Illustrator -- for free!)

Inkscape has a great vector tracing module based on Potrace. It gives you several options; I used the "Color Quantization" mode to get a vector tracing of the ? bitmap image.

Step 5: Importing and Embossing

From Inkscape, I could then export the vector tracing as a DXF file. Inventor can import this as a sketch; with some scaling and rotation I lined it up with the triangular face and used the Emboss function to engrave it into the face.

Step 6: Model Completed

After the face was embossed, it automatically propagated to all sides of the icosahedron. The -20 is born! A quick run on the Objet 3D printer at Pier 9 shows a proof-of-concept.

Still some work to do: the lines outlining the mouth are too fine and were a little lost. Also using a more contrasting resin or paint inside the embossing would bring out the shape even better. But for those times when nothing is coming up roses, this is the die to roll.