verbatimtex
\documentclass[12pt]{article}

% \usepackage[mathlf,minionint]{MinionPro} \usepackage[T1]{fontenc} \usepackage{textcomp}

\begin{document}
etex

def whiteCircle(expr p, b) =
begingroup
	fill fullcircle scaled b shifted p withcolor white;
	draw fullcircle scaled b shifted p;
endgroup
enddef;

def blackCircle(expr p, b) =
begingroup
	draw p withpen pencircle scaled b;
endgroup
enddef;

vardef TEX primary s =
   write "verbatimtex"                    to "mptextmp.mp";
   write "\documentclass[12pt]{article}"  to "mptextmp.mp";
   %write "\usepackage[T1]{fontenc}"       to "mptextmp.mp";
   %write "\usepackage{amsmath,amssymb}"   to "mptextmp.mp";
   write "\begin{document}"               to "mptextmp.mp";
   write "etex"                           to "mptextmp.mp";
   write "btex "&s&" etex"                to "mptextmp.mp";
   write EOF                              to "mptextmp.mp";
   scantokens "input mptextmp"
enddef;

beginfig(1)
	u := 1.7cm;

	picture hexagon;
	hexagon := nullpicture;

	pair A[], B[];
	numeric n; n:=6;

	for i=0 upto n-1:
		A[i] = u * right rotated (i*360/n);
	endfor;
	A[n] = A[0];

	% Shading of positive triangles.
	addto hexagon contour (0,0) -- A[1] -- A[2] -- cycle withcolor 0.9white;
	addto hexagon contour (0,0) -- A[3] -- A[4] -- cycle withcolor 0.9white;
	addto hexagon contour (0,0) -- A[5] -- A[6] -- cycle withcolor 0.9white;

	for i=0 upto n-1:
		addto hexagon doublepath A[i] -- A[i+1];
	endfor;
	
	addto hexagon doublepath A[0] -- A[3] withcolor 0.7white;
	addto hexagon doublepath A[1] -- A[4] withcolor 0.7white;
	addto hexagon doublepath A[2] -- A[5] withcolor 0.7white;

	addto hexagon contour fullcircle scaled 4bp    shifted A[1] withcolor white;
	addto hexagon doublepath fullcircle scaled 4bp shifted A[1];
	addto hexagon contour fullcircle scaled 4bp    shifted A[3] withcolor white;
	addto hexagon doublepath fullcircle scaled 4bp shifted A[3];
	addto hexagon contour fullcircle scaled 4bp    shifted A[5] withcolor white;
	addto hexagon doublepath fullcircle scaled 4bp shifted A[5];

	addto hexagon doublepath (0,0) withpen pencircle scaled 4bp;
	%addto hexagon doublepath A[0] withpen pencircle scaled 4bp;
	%addto hexagon doublepath A[2] withpen pencircle scaled 4bp;
	%addto hexagon doublepath A[4] withpen pencircle scaled 4bp;
	%addto hexagon also TEX("$\star$");

	pair X, Y, U, V, R, S;
	X := (1.5u, 0);
	Y := (1.5u, u*sqrt(3)/2);
	U := (0, -1.5u);
	V := (1/2u, -1.5u);
	R := (0, +1.5u);
	S := (u, +1.5u);

	pair hexUpRight, hexDown, hexRight;
	hexUpRight := A[1] + A[0];
	hexDown := A[4] + A[5];
	hexRight := A[0];

	draw hexagon;

	label(TEX("$\star$"), A[0]);
	label(TEX("$\star$"), A[2]);
	label(TEX("$\star$"), A[4]);

	pair triangleTop, triangleLL, triangleLR;
	triangleTop := 1/2[(0, 0), (1/2[A[1], A[2]])];
	triangleLL := 1/2[(0, 0), (1/2[A[3], A[4]])];
	triangleLR := 1/2[(0, 0), (1/2[A[5], A[6]])];

	%label.top(btex $t_1$ etex, triangleTop);
	%label.llft(btex $t_2$ etex, triangleLL);
	%label.lrt(btex $t_3$ etex, triangleLR);
	
	drawarrow (triangleTop+(0,u)) .. triangleTop;
	drawarrow (triangleLL-(u,u)){up} .. triangleLL;
	drawarrow (triangleLR-(-u,u)){up} .. triangleLR;

	label.top(btex $t_1$ etex, triangleTop+(0,u));
	label.bot(btex $t_2$ etex, triangleLL-(u,u));
	label.bot(btex $t_2$ etex, triangleLR-(-u,u));

	label.top(btex $1$ etex, (0,0));
	label.top(btex $3$ etex, A[0]);
	label.top(btex $1$ etex, A[1]);
	label.top(btex $1$ etex, A[2]);
	label.top(btex $4$ etex, A[3]);
	label.top(btex $2$ etex, A[4]);
	label.top(btex $2$ etex, A[5]);
endfig;

end