u:=1cm;

beginfig(1);
z0=(0,0);
z1-z0=z3-z2=z4-z3=z5-z4=z7-z6=z8-z7=z9-z8=z11-z10=u*dir0;
z3-z0=z7-z3=z10-z7=u*dir-90;
draw z0--z1--z4--z5--z9--z8--z11--z10--z7--z6--z2--z3--z0;
endfig;

beginfig(2);
z0=(0,0);
z1-z0=z3-z2=(sqrt5)*u*dir0;
z2=z0+(sqrt5)*u*dir-90;
draw z0--z1--z3--z2--z0;
endfig;

u:=0.3cm;
t:=2pt;

beginfig(3);
for i=1 upto 7:  draw (i*u,0)--(i*u,8*u);  draw (0,i*u)--(8*u,i*u);  endfor
pickup pencircle scaled t;
draw (0,0)--(0,8*u)--(8*u,8*u)--(8*u,0)--(0,0);
draw (0,0)--(8*u,3*u)--(0,3*u);
draw (3*u,3*u)--(5*u,8*u);
endfig;

beginfig(4);
for i=1 upto 12:  draw (i*u,0)--(i*u,5*u);  endfor
for i=1 upto 4:  draw (0,i*u)--(13*u,i*u);  endfor
pickup pencircle scaled t;
draw (0,0)--(0,5*u)--(13*u,5*u)--(13*u,0)--(0,0);
draw (0,0)--(13*u,5*u);
draw (5*u,2*u)--(5*u,5*u);
draw (8*u,0)--(8*u,3*u);
endfig;

u:=0.45cm;
path hexagon;
hexagon := u*dir0--u*dir60--u*dir120--u*dir180--u*dir-120--u*dir-60--u*dir0;

beginfig(5);
for i=-2 upto 2:
	for j=-(2-abs(i)/2) step 1 until (2-abs(i)/2):
		draw hexagon shifted (3*i*u/2,(sqrt3)*j*u);
	endfor
endfor
endfig;

end;