Felix's 16-hedron

Felix made a 16-hedron out of just triangles.

Here's another picture of it, form the Internet:

All of the faces are triangles. We wondered what kind of dice it would make. Would it be fair?

We weren't sure. There are eight faces at the end, like a pyramid and eight round the middle. Would the dice land on the end ones and the middle ones equally? 

Felix knew. He showed us that the shape would not stay on the end triangles; it overbalances.

Apparently, Felix's shape is one of eight "deltahedrons" - solid shapes made of these triangles that can land on any face separately. We're searching for the others...