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![[asy] unitsize(.5cm); pair bar(pair a) { return (a.x,-a.y); }; pair A[] = { (6.5,0),(1.5,12) }; pair P[] = { A[0],A[1],-bar(A[1]),-bar(A[0]),(2A[0]-bar(A[0]))/3,(2A[0]+A[1])/3, (5A[0]-4bar(A[0]))/9,(5A[0]+4A[1])/9 }; pair D[] = { (2P[4]+P[5])/3,(P[4]+2P[5])/3 }; draw( D[0]--P[6] ,blue+1mm); draw( D[0]--P[4] ,blue+1mm); draw( P[6]--P[4], black+1mm); pair E[] = {(D[0]+P[6])/2,D[0] + P[6] - P[4]}; dot(E[0]);dot(E[1]); draw(P[6]--E[1],red+1mm); draw(P[4]--E[1],red+1mm); draw(P[4]--P[5]); draw( D[0] -- E[1]); draw(D[1]--P[7]); draw( P[3] -- P[0] -- P[1]) ; for(int i=0;i<10;++i) { if(i<4) { } else { dot( (i<8) ? P[i] : D[i-8] ); } }; [/asy]](http://latex.artofproblemsolving.com/1/a/c/1acf167ef6b59f80eac30a664b77b608ac3cd9ea.png)
