?? "can you define multiplication of natural numbers in terms of "relatively prime" ?" as maybe good example ... ???

?? also defining anything in terms of successor ... ??? ...

?? all possible ways of decorating triangle .... ??? "special" such ... ???? hmm, confusion ... ??? .... ?? taking seriously idea of "frame-x orientations as x's" .... ?? hmmm, yet another horrible confusion here ?? ... "active vs passive" ... hard to explain without good pictures here .... ??? ....

??? each of the three frame-point orientations has a very different look when portrayed in the "collection of all frames exhibiting that orientation to given point p" style .... ??? .... ?? to what extent does this generalize ?? .... ???? .....

(?? vs ... "collection of all points exhibiting that orientation to given frame f" style ..... ????? ..... ?? hmm, that style as unhelpful (?? ...) here because whole point is that concept of frame is here (???? .....) coming equipped with canonical (??? ....) way of drawing it ..... ??? ... os ???? .... ?? hmm, hint tha answer to "to what extent does this generalize ?" above is something like ... ??? to the general context where the base carriers are plain old (?? finite ?? ...) sets, so that concept of frame has somewhat good canonical pictorial representation ... ??? or beyond that, to general context where _you've already settled on a good way to draw a frame_, and you want to use it to get good ways of drawing other structures .... ???? ...... ??? then ... ?? general idea of getting picture in which the symmetry group acts "fixed-point-free" on some orbit, so that marking single point on that orbit gives good decoration corresponding to "frame" ... ??? ...)

3 looks : "hypotenuse-to-hypotenuse", "short-side-to-short-side", "touching at only one point" .... ??? .... any nice way to single out one of these ??? ..... ???? ....

?? trying to get straight "classification of the equivalence classes of special decorations that all others can be reduced to" .... ???? nice way of getting exactly one representative of each symmetry class .... ???? ....... if that can be done ... nicely ... .... ???? .....

?? idea of having the special representative being giving each coset its own color ???? ..... color choice issue though .... ??? ....

(??no ??) paradox / confusion concerning .... ??? "distinctive" nature of "orientation classes of frames towards given x" vs "indistinctive" nature of "orientation classes of x's towards given frame" ??? .... ?????