Finally got a cube assembled out of 6 ULTiM8x8 (8x8 APA102) RGB LED panels by +Wyolum and @Maniacal_Labs_LLC ! Got it 3D mapped and running on an ESP8266.
It’s assembled using 3D printed corner brackets, hex nuts and bolts, and copper tape. The wires (5V, GND, DATA, CLK) run out of the bottom. Need to 3D print a base for it next.
Thanks everyone! Fantastic idea, @Juergen_Bruegl ! I was thinking about a rotating base, and just preventing it from twisting more than 360 degrees.
@Chad_Eby , I just started with a simple diagram of how the LEDs in each panel are ordered (serpentine from the top left), and what order the panels were assembled into the cube. Then I threw together this spreadsheet with the x, y, and z coordinates for each LED: Ultim8x8 Cube Mapping - Google Sheets missing/deleted image from Google+