I wrote:

The x,y,z coordinates of the four points, in order, are:

-1.000000,-1.000005, 0.995590 1.000000,-0.994135, 0.995590 1.000000, 0.997070,-0.992659 -1.000000, 0.997070,-0.998520

I'm a little puzzled by these numbers. If I understand my code of two years ago correctly, two of the three coordinates of each point should always be exactly -1 or +1, and the third should always be strictly between -1 and +1.

That part I have solved. I had forgotten that I was moving the points to make their centroid the origin. In this case that was a very small move. The original coordinates are: -1.000000,-0.997075, 1.000000 1.000000,-0.991206, 1.000000 1.000000, 1.000000,-0.988249 -1.000000, 1.000000,-0.994110 Of course that can't explain the bad area numbers. But for the first time I'm convinced that it is indeed my area numbers that are wrong, not someone else's. Sigh. I never should have rushed to get those numbers to James Propp before his talk. I usually test thoroughly before saying anything.