Prep the LEDs
Use a utility knife to carefully remove the silicone sheathing and most of the covering and glue from the ends of your 1M Dotstar LED strip where the connector is soldered on. Get the ends as clean and tidy as you can. De-solder the wires that came with your Dotstar strip, we'll be using more flexible wires instead.
Go to the "in" end and count out 36 pixels. Count them once more. Then, with tiny scissors or a utility knife, carefully cut between the pixels. Cut very close to pixel #36, leaving the copper pads on the side that now starts with pixel #37 (this is the "in" side and you'll need to solder on this end).
Tubing & Caps
Lay out your battery and Teensy and switch alongside your LEDs and tubing to visualize how everything should be sized. You want the switch all the way at one end of the tube, and the USB port on the Teensy all the way at the other end. A tight fit will help make sure your poi don't slip around and get damaged as you spin them.
Cut the dowel and tubing to the right length, leaving a little room to attach the leashes. My dowels ended up at 7 3/8" and my tubes came to 12".
The end caps are designed to sit flush with the top of the on/off switch so the poi won't get accidentally turned on or off in the switch gets bumped while you're spinning.
You can print them in either ABS or PLA -- the PLA is slightly stronger and will hold up a little bit better to whacks and bumps.
If you don't have access to a 3-d printer, you can order the caps from Shapeways.
For the leash end, drill a couple of holes in the tubing about 1/2" from the end. Thread your leash through the holes and tie it off securely. Melt the end of the cord to ensure that knot will never slip.