Laser Cut Acrylic (2.6 mm thick I believe, but you can double check the slot measurements in the DXFs to be sure) 

Accordign to the following DXFs.

https://drive.google.com/file/d/0B_2xkbzRozdxbHZLQ...

Solder the ends of each ring of WS2811's together, making sure to have common ground/single source power or the other way around to ensure proper power distro.

Serially connect the digital in/out lines to make one large chain. 

Wire up the buck regulator to power and the strips, and the digital in to the Arduino (or teensy, or micro of your choice). 

Have fun coding some things. Adafruit Neopixel code should work with these LEDs, http://learn.adafruit.com/adafruit-neopixel-uberguide/arduino-library