D20 Duncecap

Solidworks practice project.
Process outlined below.

Golden Rectangle

Icosahedrons are really cool shapes even outside application as dice. I'll explain why at the end. For now I start with a golden rectangle.

Duplicate Rectangles

Two additional golden rectangles are created using body move copy adding 90° rotation on two axes each. Center points are all coincident. Icosahedrons have 12 vertices and these rectangles set up perfectly for them.

Surface Loft

The vertices
connecting to their closest neighbors forms an equilateral triangle.

More Surface lofts

Now there's enough surfaces to reach opposite poles.

Pattern

Rotational symmetry keeps workflow flowing.

Setting up for a trim

The number here is purely stylistic, but also responsible
a revision. It determines how low the cap sits on the die.

Trim set

The trim tool only has a few criteria, and a large cylinder fulfills all of them.

Trim Results

The cavity is ready.

Brim

Surface fill.

Cone

The cap sits normal to the d20's up plane but points 5° off at the tip.

Finished model

Why Isosahedrons are such cool polygons

The short side of the golden rectangle in the first step is the exact same length as the edges between vertices on the isosahedron. Using that, I built the model in a manner which allows for rapid iteration through changing global variables.

If you would like to shame your dice, but have a die with an edge length not equal to 0.525 inches, you can set the sizing variable to the edge length in solidworks.