\documentclass{standalone}
\usepackage{luamplib}
\begin{document}
\mplibtextextlabel{enable}
\begin{mplibcode}
input colorbrewer-rgb
vardef make_image(expr P, n, u, v, s, arrows) =
save currentpicture;
picture currentpicture;
currentpicture := nullpicture;
for i = -n upto n:
for j = -n upto n:
draw P shifted (i * u + j * v);
endfor
endfor;
if arrows:
interim ahangle := 20;
drawarrow origin--u dashed evenly scaled 1/2 withpen pencircle scaled 1/4 withcolor Reds 8 8;
drawarrow origin--v dashed evenly scaled 1/2 withpen pencircle scaled 1/4 withcolor Blues 8 8;
draw origin withpen pencircle scaled 1;
fi
clip currentpicture to s;
draw s dashed withdots scaled 1/2;
currentpicture
enddef;
beginfig(1);
path hexagon, triangle; pair u, v; numeric n;
triangle = for i=0 upto 2: (0, 16) rotated 120i -- endfor cycle;
hexagon = for i=0 upto 5: (0, 16) rotated 60i -- endfor cycle;
u = point 0 of triangle - point 1 of triangle;
v = u rotated -60;
path s; s = superellipse(89 right, 89 up, 89 left, 89 down, 0.78);
n = 8;
picture P[];
P3 = make_image(triangle, n, u, v, s, true);
P6 = make_image(hexagon, n, u, v, s, true);
picture T; T = image(
path t'; t' = triangle reflectedabout(point 0 of triangle, point 1 of triangle);
fill triangle withcolor Reds 8 2;
fill t' withcolor Blues 8 2;
draw triangle;
draw t';
);
P4 = make_image(T, n, u, v, s, true);
picture H; H = image(
path ha, hb;
ha = hexagon reflectedabout(point 0 of hexagon, point 1 of hexagon);
hb = hexagon reflectedabout(point 0 of hexagon, point 5 of hexagon);
fill hexagon withcolor Oranges 8 2;
fill ha withcolor Blues 8 2;
fill hb withcolor Greens 8 2;
draw hexagon; draw ha; draw hb;
);
P7 = make_image(H, n, u zscaled 1.732 dir 30, v zscaled 1.732 dir 30, s, true);
picture dualt, dualh;
dualt = image(
draw triangle withcolor 1/2;
for i=0 upto 2: draw origin -- point i+1/2 of triangle withcolor Reds 7 6; endfor
draw currentpicture reflectedabout(point 0 of triangle, point 1 of triangle);
);
dualh = image(
draw hexagon withcolor 1/2;
for i=0 upto 5:
draw origin -- point i+1/2 of hexagon withcolor Reds 7 6;
endfor
);
P5 = make_image(dualt, n, u, v, s, false);
P8 = make_image(dualh, n, u, v, s, false);
