Deconstructing flies
Naturals:`long (1)X, short (2)Y, Long (1)Z in calls or puts via verticals.
Combos: long Y straddle; short X, Z strangle (synthetic or iron fly).
132 asyms: long (1)W, short (3)Y, long (2)Z with the bull vert at twice the strike-width of the bear vert.
Call asyms and put asyms are equivalent, but for microstructure you'll typically trade whichever has more OTM legs.
Synthetic asyms: the 132 asym is a one lot bull vertical (to buy) and two lot bear vertical. The box arbitrage dictates that bull(bear) call and put spreads trade equal, so you can construct the asym 132 (or any ratio) as OTM verticals.
132 asym fly in calls: long (1)100C, short (3)200C, long (2)250C. Dissected as a one lot 100/200C bull spread and two 200/250C bear spreads. Call and put verticals are equivalent (boxarb) so you can also trade the synthetic, via the combo, by shorting the 100/200PS and short two of the 200/250CS (call spreads).
Flies are either verticals (naturals) or a combination of puts and calls (as in vertical vs. iron fly).
You can see that the above synthetic asym would become an asym-synthetic (iron) condor if the center strike became a split-strike.
We'll get into structuring later, but the choice of fly vs. condor will depend on skew, stickiness, etc.