Acrylic Fan Base
I found this acrylic plastic in the discount bin at my local plastic store for $2/sheet. They have all shapes and sizes and thicknesses. Sign-making shops often have material available. As long as your plastic is sturdy enough and at least 1/8" (3mm) thick, you don't need to be too picky.
Decide what size you'd like your fans to be. Mine have roughly an 18" diameter.
Trace out your pattern on the acrylic sheet. With a band saw or a multi tool with a cutting wheel (or a laser cutter if you're getting fancy), carefully cut out the fan shape and the cutout for your fingers. Don’t use a drill for the finger cutout unless you have a special acrylic-cutting bit. After cutting the shapes, play with the fans a bit and sand down any pokey edges.
If you don't have access to power tools or laser cutters, your plastic store will be happy to cut these for you for a fee.
The enclosure isn't necessary, but it will protect your battery and Pro Trinket from bumps and knocking about, and extend the life of your fans.
If you have access to a 3D printer, you can download the electronics enclosure from Thingiverse:
Print in PLA or ABS. Since I'm using a silver veil fabric on the fans, I printed the enclosure in white.
If you don't have a 3D printer, you can order a custom enclosure from Shapeways, or you can simply glue the Pro Trinket and battery directly to the acrylic fan.
Attaching the LEDs
Align the Dotstar strip around the outer edge of the fans, and carefully cut through the strip at the right length. Count how many LEDs you have -- mine have 38.
Find the "in" end of the Dotstar strip and solder about 6 inches of wire to each pad. It's a good idea to use a different color of wire for each pad. That will make it much easier to keep them straight when you solder the lights to the Pro Trinket.
Test the strand by hooking up the wires to your Pro Trinket with alligator clips and running the Dotstar strandtest example — this is explained at the bottom of "The Code" page of this guide. Be sure your strip is working and all the LEDs are in good shape before attaching it permanently to your fans.
Set the acrylic fan on top of some supports so its edge is hovering about 1/4" from the table. (The leftover acrylic you just cut off works great as a support). Line the Dotstar strip against the edge so it's centered both up and down, and left to right.
Run a bead of DevCon Silicone Glue along the edge of the fan where it's touching the Dotstar strip. With a gloved fingertip or tool, smooth the glue into the corner so that it contacts both surfaces as much as possible.
Also add a little glue inside both ends of the Dotstar silicone case to seal it up and keep your soldering secure.
Let the glue dry completely overnight, and repeat with the other side.
Adding the Enclosure
Place the plastic enclosure along the edge of the fan about halfway between the edge of the fan and the handle cutout, and glue it down. Hot glue works great for this. Place it so that the wires from the Dotstar strip reach comfortably, but it's far enough away from the handle that it doesn't get in your way while holding the fan.