A dodecahedron is a polyhedron with 12 faces. In particular, this is the regular, convex, non-stellated dodecahedron, which is one of the Platonic solids, and is composed of 12 regular pentagons. Link to Wikipedia article here.

The model provided uses regular pentagons with a side length of 1 fuselage unit. It was constructed through exact position and size calculations, which gives the model 100% accuracy.

To briefly describe the construction methodology, the regular pentagon--the shape that composes the 12 faces of this structure--was first created, then angle and position calculations were done to align the sides faces of the shape. Finally, the radius of the inscribed sphere was used to calculate position of the "mirror" face, that is, the top half.

For more extensive documentation on the process, please use the links below (three parts):
Part 1 | Part 2 | Part 3

So I ended up creating another Platonic solid. The bucky ball is proving difficult to make, so I took some time off and went ahead with making this. To be frank, the math proved to be more finicky than I thought. Good practice though!

Hope this is useful. Maybe for DnD dice?
- Snow