Hellraiser Lament Cube Dice Box, holds 3 of the 7 dice set boxes, on my profile.  81mm (3ish inch) cube.

Each side of the small dice boxes are roughly 12mm tall, which means you will have about 20mm height for dice. This will hold most standard size dice, it might not support all dice, especially non standard one. However if you find your dice not fitting you can increase the size to fit your specific dice. 

Tolerances vary from printer to printer, different types of filaments, I have personally printed this over 400 times, and have over 200 prints and downloads on Maker World.