Various crystallographic space groups
Only a few of these illustrations made it into The Symmetries of Things, but there aren’t such constraints here, and so I present a whole lot of pictures of the non-isotopic, or “composite’ crystallographic symmetries. Eventually I’ll add all that I have to this page, and label the figures correctly.
These were all drawn as straight up postscript programming in a few kilobytes of code that can be computed directly, as a program (!), within a laser printer.
For the best viewing pleasure, double click on an image and scroll through the lightbox.
Match each illustration to its coupling, with the generators below. From the coupling the rest of the data follows.
These symmetries fiber over the Klein bottle (!)
Match each illustration to its coupling, at left, and thence to its Intern. no. and Thurston-Conway fibrifold name.
Exercise: There are more illustrations than couplings. Which are redundant?
Let me know.
Quiz: which three of these symmetries are missing figures?
Match the figures with the couplings!