Wolfram Language (Mathematica), 232222 bytes
n=6;c=Graphics[{#,Rotate[Polygon[CirclePoints@6]Rotate[Polygon@CirclePoints@6,30Degree]}, ImageSize->9]&;
Column[Row>9]&;Column[Row/@TakeList[(Mod[Tr@DigitCount[#Tr@DigitCount[#,2,1],2]&1]~Mod~2&/@Reverse@Select[Tuples[Range[0@Reverse@Select[Range[0,2^nh=2^n-1],3]1]~Tuples~3,Tr@#==2^n-1&]Tr@#==h&])/. {1->c@Red,0->c@Yellow>c@Blue},Range[2^n]],Center,.01]
I believe that this is NOT code-golf...
If OP decides that it is, then I will golf it