?? so (P,*)-spectrum can (?? reflecting further on the "ray cone as direction in which you can go to infinity ..." idea ... ???? ....) be seen as some sort of "poincare dual" of fan ??? ...?? only "schematically" so far, but ... ?? .... then (R,*)-spectrum as ... ??? some copies of this glued together in way involving lattice .... ??? ... ?? change of lattice ??? ... ??? ....

??? weylotope as example here ... ?? vs as example of that other idea ... toric projective embedding ... ??? multi-projective ??? .... ?? weylotope degeneration vs scaling ... ??? .... each root independently ... ???? .... ???? ...

?? polytope edge as blow-up of ... ??? .... ???

??? blow-up ... operad .... ??? opetope ... ??? "flat" ... ???? ....