## Another 600-cell cross-section sequence

This time, instead of translating the 600-cell along the w-axis,
I'm doing a rotation of the y and w axes, while keeping the
position along w-axis fixed. Again, since the colors of the
faces on the cross-section are inherited from the cells that they
are a cross-section of, we can use the colors as an indication
of orientation.
**All of the small thumbnail images below are links to
full-size images.**

There is not a lot that I can say about this sequence of images,
because I don't know how to account for each and every face or explain
the symmetries that occasionally arise in them. Rather, the one basic
fact that is pretty obvious, and which I can explain, is that as the
rotation progresses, we see a greater and greater range of colors
appear on the faces of the cross-section. This is because the
rotation is gradually bringing points that originally lay on the
w-axis to lie in the x-y-z hyperplane. As the magnitude of their
w-coordinates is being lowered down to zero, more and more of the
color map which extends along the w-axis is made visible by cutting
along the hyperplane where w=0. At the end of the rotation through 90
degrees, these antipodal points have a zero w-coordinate, and we see
the broadest range of color. Also, note that points which had x or z
coordinates of zero are unchanged by this rotation, so the medium
green faces which form a vague band around the final cross-section
are from cells which lie close to or in the the x-z plane.

Note that the geometry of the last cross-section is the same as that
of the first, though the orientation in space is different. What
does that say about a symmetry of the 600-cell?

Here is another view of the 8th cross-section shown above (rightmost
one on the third row):