So, apparently, Dice Towers are a thing.
There are many Dice Tower design / construction videos on Youtube. Here are a couple of pictures from some I found. The problem with these designs is that they are made from foam. The one on the left is made with a foam core / glue gun construction with EPS foam blocks then cut and glued on. While the paint job is very cool, the light foam board construction is going to sound silly when you toss in the dice. The one on the right uses EPS foam blocks glued around a vase and a spiral ramp of foam core inside to bounce the dice around. Again, this one will just sound silly as it’s used.