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This is a design I made in 2020 but never posted it outside GitHub. The original version had an external controller box with an Arduino Nano running a custom firmware, but I recently designed a nicer stand that contains a D1 mini ESP8266 running WLED.
The cube is 23cm wide.
3D printed parts
6x beam
2x beam-w-hole
2x beam-bottom (one symmetry !)
2x beam-bottom-w-hole (one symmetry !)
4x corner
4x corner-bottom
5x corner-cache
1x corner-cache-w-hole
4x panel-holder
1x electronics-case-support
use the alt version if you don't want to include a push-button
Hardware
6x 210mm/2mm square one-way mirrors (or standard glass/PMAA with one-way film)
24x M2 15mm conical screws
Electronics
6x 80cm WS2812 LED strips (60 LEDS/m)
1x Wemos D1 mini
1x 16mm push button
1x female DC jack with terminals
1x 5-10A 5V power supply
Assembly
Start building the cube from the top panel, taking care where you use beams with or without holes to pass the wires. You will use all beams and corner pieces and five panels, dont put the last bottom panel yet
Cut the LED strips to length en solder the wires, I recommend using dedicated power lines for each strip but you can use a single wire for the data line
Glue the strips to each side and pass the wires in the beams, all wires must output on the same corner. I recommend adding CA glue as the standard 3M tape is not adhesive enough
Check that every strip is working correctly
Put the bottom panel and secure it in place by glueing the four panel holders
Glue all height corner caches
The following diagram shows one way to arrange strips (flattened cube seen from top).
Software
I recommend to install WLED. Don't forget to divide the maximum power output by 6 as all the strips are in parallel.