How to paint a tetrahedron (idea) by 1010011010

Q: How many different ways can you paint a tetrahedron using no more than 4 colors?
A: 36

Unfold a tetrahedron so you get four triangles in the fashion of a first iteration Sierpinski triangle.

             /\               
            /  \              
           /    \             1234  1234  1234  1234
          /      \            BBBB  BBBG  BBBR  BBBY
         /    1   \           BBGG  BBGR  BBGY  BBRR
        /          \          BBRY  BBYY  BGGG  BGGR
       /____________\         BGGY  BGRR  BGRY  BGYR
      /\            /\        BGYY  BRRR  BRRY  BRYY
     /  \          /  \       BYYY  GGGG  GGGR  GGGY
    /    \    2   /    \      GGRR  GGRY  GGYY  GRRR
   /      \      /      \     GRRY  GRYY  GYYY  RRRR
  /    3   \    /    4   \    RRRY  RRYY  RYYY  YYYY
 /          \  /          \   
/____________\/____________\

Like most of my dreams, that one was licensed for commercial use	I was never any good at maths at school	symmetry groups of the Platonic solids	group acting on set
Deltohedron	Sierpinski triangle	tetrahedron	If someone asks you if you're a god, you say, "Yes!"
fixed point formula for a finite group acting on a finite set	Combinatorics	The math Project	ASCII art
bugger	Having to sit next to my ex on my flight from Chicago	alternating group	Morality Films
Absolute Zero	Mobius number	Star Wars Holiday Special	The possible surpasses the actual
hologram	Hanging paintings on burning walls	reindeer tears	The Everything and Nothing Manifesto