\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;
    hexagon  = for i=0 upto 5: (0, 16) rotated  60i -- endfor cycle;
    triangle = for i=0 upto 2: (0, 16) rotated 120i -- 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);

    draw P3 shifted (-100, +100);
    draw P4 shifted (-100, -100);
    draw P5 shifted (-100, -300);
    draw P6 shifted (+100, +100);
    draw P7 shifted (+100, -100);
    draw P8 shifted (+100, -300);
endfig;
\end{mplibcode}
\end{document}