
Fundamental domains for nonarithmetic latticesThe following are projections of 4dimensional polytopes that appears in my joint paper with J. Parker and J. Paupert. The polytopes are invariant under a regular elliptic element (of order 7, 8 or 30 depending on the group), so they are actually a bit bigger than fundamental domains. There are twelve groups, hence twelve polytopes; for each polytope we show two projections of the 1skeleton, onto each of the invariant complex lines of the regular elliptic element (the projections are displayed on the left for one axis, on the right for the other). Among the 12 lattices, only two are arithmetic (can you spot them? :D) Here is a picture of some individual faces.
