Each face is identical. It's made by taking a golden rectangle and connecting the midpoints of each edge which results in a diamond shape:
Here's the one I made from 1/2" thick walnut and ash. It's about the size of a volleyball.
It’s actually held together with magnets – 120 of them – one in each edge.
Vacuum pressure comes through the table and fixture to hold it in place. Two tiny pins prevent it from twisting during the cutting and drilling.