Disclaimer: I'm not a mathematican. Please answer in a way a non-mathematican can understand. Thank you.
I'm building kind of a wooden puzzle and got stuck. My problem is: I have squares whose 4 edges have x different key-and-slot-patterns. Each square looks the same. Now I can join different squares to each other (edge-to-edge) as long as the edges don't share the same key-and-slot-pattern. I prefer to see the keys and slots as a "color". That way each square has x colors whose edges can be joined to each other as long as their color differentiates. Joining may happen planar or perpendicular. In a first step I want to build a cube whose 6 faces consist out of 6 squares. I want to know how many different edge colors I need when building a) an ordinary cube b) a cube in cube system like the rubic's cube (3x3x3). Can anybody give me a tipp where to start?
Here's a picture of the "keys-and-slots" and the resulting cube: