How many colours at least do you need to paint that so that no two adjacent faces are identical?
P̶r̶o̶b̶a̶b̶l̶y̶ ̶1̶2̶,̶ ̶a̶s̶ ̶i̶t̶ ̶i̶s̶ ̶a̶ ̶d̶o̶d̶e̶c̶a̶h̶e̶d̶r̶o̶n̶.̶
Scratch that, I didn’t understand your question completely.
Wow, I flashed on Jodie Foster in the middle there. Seemed like a lifetime!