This is a remix from a model on thingiverse https://www.thingiverse.com/thing:2124983

I added more space for the LED ring wires since the Adafruit LED ring has wires all around the ring unlike the ones that the original author used.

Items used:
Adafruit Pro Trinket - 3V 12MHz - https://www.adafruit.com/product/2010

Adafruit LiIon/LiPoly Backpack Add-On for Pro Trinket/ItsyBitsy - https://www.adafruit.com/product/2124

Lithium Ion Battery - 3.7V 2000mAh - https://www.adafruit.com/product/2011

NeoPixel Ring - 16 x 5050 RGB LED with Integrated Drivers - https://www.adafruit.com/product/1463

Hook-up Wire Spool Set - 22AWG Solid Core - 6 x 25 ft - https://www.adafruit.com/product/1311