Properties of the plot marker shapes

In answering this question, I realized that I do not understand how MATLAB defines its markers in plots. For a marker of a given size plotted at a point (x,y), what defines where it will be "centered" and its width and height?

If I create a square axis with x and y limits of -1 to 1 that is scale inches high and wide

scale = 4;
set(gca, 'Units', 'Inches')
set(gca, 'Position', scale*[0.25, 0.25, 1, 1])
set(gca, 'YTickLabel', [])
set(gca, 'XTickLabel', [])
axis([-1, 1, -1, 1])
axis square
box on
hold on

and then plot all the symbols to be scale*72 units big (since there are 72 points in an inch)

plot(0 , 0, '.', 'MarkerSize', scale*72);
plot(0 , 0, 'o', 'MarkerSize', scale*72);
plot(0 , 0, 'x', 'MarkerSize', scale*72);
plot(0 , 0, '+', 'MarkerSize', scale*72);
plot(0 , 0, '*', 'MarkerSize', scale*72);
plot(0 , 0, 's', 'MarkerSize', scale*72);
plot(0 , 0, 'd', 'MarkerSize', scale*72);
plot(0 , 0, 'v', 'MarkerSize', scale*72);
plot(0 , 0, '^', 'MarkerSize', scale*72);
plot(0 , 0, '<', 'MarkerSize', scale*72);
plot(0 , 0, '>', 'MarkerSize', scale*72);
plot(0 , 0, 'p', 'MarkerSize', scale*72);
plot(0 , 0, 'h', 'MarkerSize', scale*72);

I get the following result

The documentation say . is plotted at 1/3 the size. If you scale it up, then . and o are the same size.

It doesn't appear that the symbols are equal diameter, radius, or area. I don't think they are equal circumference (although I haven't proven that to myself yet). It looks like they might be centered on the center of gravity, but again I have proven this yet.

Do the marker sizes and locations make sense from a graphical representation standpoint?