?? kaleidoscope as _co-fan_ ... ??? ....

?? hmmm ... ?? vague memory of ... ??? having some reasonable visual intuition about co-fan while talking to baez on his last visit here ... ?? in car and hotel room ... ?? at least, visual intuition about co-face .... ???? .... ?? actually more tactile than visual ?? .... feeling edge (?? ...) of 3d object .... ????? .....

??? given face of cocone, corresponding coface of it

??? vague intuition about "infinitesimal neighborhood of face" .... ??? or "localization" ????????? ..... ?? "the only constraints that you keep are the ones that "touch" the given face" .... ????.... ?? "that touch face f" = "for which f lies completely on border hyperplane" here ... ??? ...

?? hmmm, sort of "flower" picture of 2d (maybe higher too ???) co-fan ??? ... ?? "spirograph" ??? ... ??? dual fan ???

?? hmm, maybe "flower" (with nicely separated (??...) petals (?? = cocones ?? ...), no petal over half a circle, circle of petals closes up after just one revolution ... ????...) is more apt than "spirograph" here .... ??? hmm, or maybe "spirograph flower" is better ... hmm, actually i'm still a bit confused ... ??? ....

?? "daisy" ??? ... ??? maybe other fancy names that people who think about certain sorts of curves (??) use .... ??? ....

??spirograph flower given by "modulus as function of argument" ???.... ??? zeros of such function ... ???? ..... ?? "fourier ..." ... ???? ....

??? trying to understand toric quasicoherent sheaf in terms of spirograph flower ... ???? ....