Questions, Problems, & Conjectures about Origami Cubes

From the 2005 ReSEARCH Group

1. Question: Given x colors, 0<x<13, how many different ways can you color your cube? (A.R.)

2. Conjecture: For x amount of colors you can make your cube x amount of ways. (A.R.)

3. Discussion of the above conjecture: Initial thinking was that there would be many more than 12 ways to make a cube given 12 colors (R.B.), and that there are more than 2 ways to make a cube given 2 colors. (S.S.)

4. Question: Is it possible to make my cube so that all four colors appear on every face? (C.F.)

5. Questions: Is there an equation that will help us or tell us how many ways we can color a cube with x amount of colors for any amount of each color? (R.F.) Is there a definite amount of ways to color the cube with a definite amount of colors? (A.R.)