?? maximal affine portion of kaleidoscope toric variety v ... ??? try to understand in terms of ... v embedded in g/b .... ?? nice maximal affine portions of g/b .... associated with apartment .... ?? cover of g/b formed by such maximal portions .... pulled back aling embedding ... ??? hopefully coincide with nice toric fan-nish cover ... ???....

?? relationship between cover and cw-complex structure here ... ??? .... .... schubert calculus ... ??? .... ???? ......... double role of schubert varieties .... giving nice special representatives of cohomology classes, vs cutting (??) variety into pieces of open cover ... ??? .... ??? confusion / paradox here ??? ... ?? "cutting" as requiring real co-dimension 1 .... ????? ......