Infinity Mirror cube but its a dodecahedron 

Does require some non 3D printed parts and some parts orientation

3D printer parts count
Dodecahedron Corner inner x19
Dodecahedron Corner inner hole x1 (for wires to come out
Dodecahedron Corner outer x19
Dodecahedron Corner outer hole x1 (for wires to come out
Dodecahedron Edge inner x 30
Corner Stand x1
LED cover (optional) x30
 

Non 3D printer parts
Pentagon mirrors (acrylic with 2 way film applied) x12 (edge length = 144mm)
M3 black countersunk screws (8mm but 10mm might work) + nut x60
LED strips 133mm (8 leds at 60Led Per Meter) x 30
Power supply (5V 3A min, more is better)
Arduino or other microcontroller

Build tips
There are holes designed for 1.75mm filament to be used as dowel between inner edges and inner corner pieces, but this isnt great by itself so build one pentagon at a time with the outer corner pieces holding it together with the screws

Soldering the LEDs can be fiddley, try to connect 5V and GND at all connections in the corner to reduce voltage drop across the design. 

The data line will sometimes have to double back but there are groves in the edge pieces for a thin wire to hide under the LED strip. Spend some time planning out the order of the LED datain/dataout positions

LED covers are optional but hide the strips text markings well, they are however just glued on as were a last minute idea. This design assume the LEDS have a sticky back too, but I had to add a bit more glue to prevent them peeling off after a time

Make sure all your LEDs are in place, soldered and working reliably before adding the acrylic panels otherwise you have to remove a lot of them to get back in easily to fix any issues