?? so ... ?? toric variety as built out of toruses, obviously ....

repercussions for examples ... kaleidoscopic, generalized (?? including stacky ...??) ... ??? ....

?? kaleidoscopic .... ?? bruhat cell, vs ... ?? ....

?? quotient torus / sub-lattice .... section / retraction thereof ... ??? ?? extra information in "fringe attachment" data ?? ..... ????? .....

?? other real forms of complex toric variety ??? ... ?? .... ??? x^2+y^2=1 ??? ....

(C,*) -> (P,*) "magnitude" ... ??? ....

??? so ... non-fullness of progression from toric to non-toric stuff ... especially, comm monoid alg hom coming from partial monoid hom with domain a "fringe" (?? ...) submonoid ...