I modeled this cube and construction jigs in fusion 360. The dome is made from acrylic, I ordered that by size and glued it together with chloroform. All black plastic was printed on my CR10S-pro and glued with chloroform. Inside the box are 4 x 60A power supplies mounted on a 4mm thick aluminum plate. Running all led's to the max will need around 1200 watt of power. I have a custom PCB with a Teensy 4.0 mounted on it. Only 3 pins of the Teensy are used to drive 32 channels with 128 leds each. The refresh rate of the display and the animations is 178 frames per second. Everything is non blocking and refreshing the display is done with DMA taking zero processor time. There also is an esp8266 and a touchscreen connected to the PCB, that will need to be programmed at a later time.
Every led was bend and cut using a 3d printed jig. All coper wire was drawn through a draw plate to work harden the copper and make it the right diameter after this the wire was straightened using a drill. All led's are than soldered on the copper wires using a 3d printed jig. That is than assembled in 16 blocks using other jigs. Everything is modular and if a led breaks in the middle I can just lift out a block and fix it....
I don't recommend making this. Led bending alone took 80 hours, designing, soldering and coding took many many more. Don't be crazy like me....