And stuck them together to make little modules:
Which I spent another hour trying to turn into a proper silly hat ...but my triangular pieces didn't have much structural integrity when trying to hold the weight of too many pieces, and it all fell apart:
I eventually packed all my pieces up and resolved to try again soon, perhaps with a different arrangement...
I also learned something on the vinyl cutter! I have an image of an astrolabe from the photo collection of Oxford's Museum of the History of Science.
The problem is, something funky happened when I vectorized my image-- and it resulted in a bunch of connected line segments rather than curves:
When I tried to print this out on the vinyl cutter, the knife kept lifting up and down and things got both slow and ugly. I stopped the vinyl cutter before it finished the run, and sure enough all the smooth edges (in blue) appeared jagged (especially compared to the smoothness of the final cut, in red):
Luckily, Oscar was there and could help me out! He suggested that I go back to the original pre-vector image and perform the following steps in Photoshop: