How would you make "pop-up" paper dice?

I am interested in placing two dice on a storyboard. The issue is that someone else will be transporting the storyboard and needs the dice to lay flat. I want to make them three-dimensional.

My first thought is to create two dice that pop up. I'm trying to think of clever ways to make them pop up without looking horrible.

I'm thinking of having some pretty stiff paper for the dice. Perhaps, I can insert some toothpick "splints" that allow the dice sides to fold outward but not inward. Finally, I could attach a rubber band to the inside of the die, so it pulls the sides inward (which stops as the splints dictate).

That's my initial plan, but I'm curious how others would do it. What materials would you seek out?