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\documentclass[border=5mm]{standalone}
\usepackage{luamplib}
\begin{document}
\mplibtextextlabel{enable}
\mplibsetformat{metafun}
\begin{mplibcode}
input colorbrewer-rgb
beginfig(1);
numeric r; r = 5;
path d; d = for i=1 upto 12:
up scaled r
shifted (r * (sqrt(3)+2), 0)
rotated 30i --
endfor cycle;
color shade[];
shade0 = Oranges 8 3;
shade1 = Blues 8 3;
shade2 = Greens 8 3;
shade3 = Reds 8 3;
vardef unit(expr n) = image(
fill d withcolor transparent (2, .9, shade[n mod 4]);
draw d;
) enddef;
pair u, v;
u = point 0 of d - point 3 of d;
v = u rotated 60;
numeric n; n = 6;
for i=-n upto n:
for j=-n upto n:
draw unit(i*j) shifted ((i - floor(j / 2)) * u + j * v);
endfor
endfor
clip currentpicture to unitsquare shifted -(1/2, 1/2) scaled (n * 9 r);
picture p; p = image(
draw d; draw point 0 of d withpen pencircle scaled 2;
drawoptions(withcolor 3/4[red, white]);
draw d shifted u; draw point 0 of d shifted u withpen pencircle scaled 2;
drawoptions(withcolor 3/4[blue, white]);
draw d shifted v; draw point 0 of d shifted v withpen pencircle scaled 2;
drawoptions();
drawarrow origin -- u withcolor red;
drawarrow origin -- v withcolor blue;
);
label.bot(p, point 1/2 of bbox currentpicture shifted 13 down);
label.bot(btex \vbox{\hsize 3.4in\noindent
The vectors are chosen so that the dodecagons overlap to make
the required triangles, squares, and hexagons.} etex,
point 1/2 of bbox currentpicture shifted 13 down);
endfig;
\end{mplibcode}
\end{document}
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