The hexagon isn't regular, so if I gave A a coordinate value of (0, 0), I still wouldn't know what the coordinates of other points would be. Here's the asymptote code:
[asy]
unitsize(1 cm);
pair[] A, B, C, D, E, F;
A[0] = (3,6);
B[0] = (5,5);
C[0] = (4,2);
D[0] = (0,-1);
E[0] = (-2,2);
F[0] = (0,5);
B[1] = (A[0] + B[0] + C[0])/3;
C[1] = (B[0] + C[0] + D[0])/3;
D[1] = (C[0] + D[0] + E[0])/3;
E[1] = (D[0] + E[0] + F[0])/3;
F[1] = (E[0] + F[0] + A[0])/3;
A[1] = (F[0] + A[0] + B[0])/3;
draw(A[0]--B[0]--C[0]--D[0]--E[0]--F[0]--cycle);
draw(A[1]--B[1]--C[1]--D[1]--E[1]--F[1]--cycle);
label("$A$", A[0], N);
label("$B$", B[0], dir(0));
label("$C$", C[0], SE);
label("$D$", D[0], S);
label("$E$", E[0], W);
label("$F$", F[0], NW);
label("$A'$", A[1], N);
label("$B'$", B[1], NE);
label("$C'$", C[1], SE);
label("$D'$", D[1], S);
label("$E'$", E[1], SW);
label("$F'$", F[1], NW);
[/asy]
Thanks for your help!
