https://stampsound.com/what-is-a-speakon-connector-cable/ for beginners

My thoughts

I'm about to convert my personal PA from the obsolete "speaker cannon" connectors to speakons.

It's a stereo amp so I'll use 4 conductor cables. The speakers are 2-way full-range boxes.

The amp will have two female output connectors wired identically, with amp channel A to cable channel 1 and amp channel B to cable channel 2. That seems obvious enough. The cables will be conventional 4-conductor straight through male to male. Again obvious. 

Then it gets a bit more complicated. The loudspeakers will each have two female connectors. One will connect channel 1 of the cable to the loudspeaker. The other is a looping point, and reverses the cable channels. We'll call this an S point (for "swap"). So cable channel 2 of the R point is connected to the loudspeaker (and therefore to channel 1 of the "normal" (or we'll call it the N point), and cable channel 1 of the S point is connected to cable channel 2 of the N point.

SO...

Simple stereo setup

Amplifier to left speaker N, amplifier to right speaker R. Done.

Or if the speakers are closer to each other than one of them (say the left channel) is to the amp, amplifier to left speaker N, left speaker S to right speaker N. Done.

Simple FOH and foldback setup

Amplifier to left speaker N, amplifier to right speaker N, either FOH S to wedge N.

Or amplifier to left speaker N, left speaker S to right speaker S, amplifier to wedge S. 

Or amplifier to left speaker N, left speaker S to wedge N, wedge S to right speaker N. (This isn't so good. For example if you want to move the wedge, or string on another wedge, but it keeps the cable runs across the stage to a minimum, which is kind of cute. Except rule 1 is, don't be cute.)

Or for two wedge strings, amplifier to left speaker N, amplifier to right speaker N, FOH S to one wedge N, other FOH S to other wedge N.

Wedge string

The last possibility doesn't allow for wedges to be in a string, as both connectors are in use. But the other two do. Just always go from S to S or N to N.

Or at least, you could string wedges by running the feed from one FOH to the other through the whole string. Cute. But don't.

Advantages

Only two connectors required per speaker box or wedge or at the amplifier, but maximum connection possibilities. All cables identically wired. All loudspeakers identically wired. Minimum cable runs. Maximum use of second circuit in the cables. No adaptors required.

Expandable without any new conventions or wiring schemes.

But it does of course still require some thought on the part of the setup crew.