OK so here are his 12 'orders of battle', formations or deployments in 40k, and how you might see them across the table plus the bonus info of how to oppose them. This really helps you with Friction, ironic since C-man and J-dude were pretty unfriendly when they hung out together.
1. Parallel Order. To Jomini this is the worst order. It introduces no sophisticated tactics it just smashes line on line until someone wins. Trouble is the reason that is bad is that forces were relatively evenly matched, in terms of tech, training etc, at the time so realistically since this isn't the case in 40k we can write that off somewhat.
You see this one most from armies with high resilience, low mobility and high destructive capability in close. Deathwing Terminators and Necron Phalanx spring to mind as well as foot Wolves, Wolf Wing, ThunderWolves or shooty Wolves. This is mostly used by people who believe the "its the list stupid!" theory of 40k, or worse "its the codex creep stupid!". The point is they have no decisive plan other than to close and bring force to bare evenly relying on inbuilt advantages to see them through.
You combat it by first deciding if you win the brawl and second using one of the more sophisticated plans if you are less than sure you do.
2. Parallel Order with Defensive or Offensive crotchet. You reduce the length of your line and form either an offensive or defensive base on one side, dictated by terrain usually. Normally this is a defensive position because you don't have a lot of paths to exploit weakness when your superior force element is in a corner.
You see this all the time. People pick a side and put down the stuff they wanna use in an attack there. It's intuitive. What isn't necessarily intuitive is why this is usually a defensive order. Lines of exploit are golden and when your strong point is the center you can exploit in all directions, which is why it's the best place to start in games like connect four and 40k when all other things are equal. You can see these lines as fire lanes or movement paths.
This one combats the first by basically forcing them to change formation to deal with you. A classic play with a maneuverable army is to deploy as order 1 then move fast vehicles to the side to resemble fig 2 before thrusting on the flank before your opponent can move to counter.
3 and 4. Parallel Order with Reinforcement on Flank (3) or Center (4). This one is quite subtle. Rather than use stronger units to concentrate your force you use waves of unit. It works well for forces that have high impact but low survivability like Stealer lists or Tau. It is my preferred order of battle to use one of these two. Against a force where I expect multiple exploits to become available I use 3, because I can diverge from the stronger center, and against forces who have monolithic units I use 4, and feed the unit my army.
You see this one less frequently. People seem to not like placing units behind each other during deployment, which I find odd. Mid battle however this one becomes popular as people consolidate force elements into a defense of objectives x and y or an attack on objective z. The beauty of this one is given sufficient mobility you can adapt to more or less any other order inside a movement phase.
You counter this by attacking the weak line while avoiding the strong reinforcement, its quite instinctive.
5. The Oblique Order. What people in 40k call flanking. The aim is to move at an angle to the opposing line and expose uneven mobility in order to concentrate superior force. The subtle fact here is that most armies don't have uneven mobility - they are either all mounted in rhinos, yawn, or move at a similar pace on foot etc to the rest of the army. You therefore must create it by shooting them out of their transports or anchoring your weak center with terrain in most cases.
This works with more or less any force with an element that concentrates well. So blast template shooting, any assault force or close range shooting like Sisters. The key here is that your units are synergistic on the front end of the line so that fighting is decisive.
You counter this by either withdrawing into a reverse of their order, out lasting their attack at the decisive point or preempting their attack with one of your own so the opposition is in a more favorable position for the remainder of your force to come into play.
6 and 7. Perpendicular order on one (6) or both (7) wings. So this is what your doing when you outflank, deep strike or play Daemons. The idea behind 6 is to roll the enemy up, rather like cavalry used to do in classical battles where as 7 is designed to divide the enemy so that you can react to mistakes. As a purely offensive position this order always gives you first strike potential which can be significant in 40k.
Guard with the Taliban dude do this superbly. Tau can get it done well as well as can Blood Angel jump pack lists. Obviously all Daemon armies do it instinctively and forces based around Crushers, Defilers and Prince are generally attempting 6, or should be, where as forces based on troops, esp Slaanesh based forces, should go for 7 instead.
The counter is very difficult. You generally hope they roll poorly for reserves or deep strike scatter and you try to take them out piecemeal. If that doesn't work you need to make a concerted attack on the weaker side, if they're doing 7, or provide a sacrificial element to the attack if they use 6 and then try to separate the force.
8. Concave in the Center. What people in 40k call double flanking. This is actually best used as a transitional plan. That means you start off defensively then at some decisive point you switch to offense and surround the other guy or move for objectives.
Best performed by shooty infantry based lists you want to present a slightly weaker center which is further back. You want the enemy to form into order 4 and attack your center at which point you have him because his strength is committed while yours is not. The danger here is that your units will be unable to reinforce one another from left to right because of the central battle or that the central battle will be over too quickly. Both of these mean that assault armies can't really use this one. Static Guard, Foot Eldar, Shooty Marines and Tau use this well.
You counter this one by being too strong on the attack essentially. Or outlasting the defensive phase so that the other guy blinks first and moves.
9. Retired Center. Is basically the same as 8 except there is a more dramatic difference in distance between the center and the wings. The idea here is that your sacrificing the center to trap the opponent against your own board edge and isolate his force there. It is best when there is terrain in the center - Agincourt style.
10. Winged Echelon. This is the perpendicular order (7) for armies without access to Outflank, Deep Strike etc. Orks with Scout moving choppers are the classic because they don't want to reserve stuff but the do want to try to divide the force before the battle wagons get there. Counter in much the same way - with difficulty or preemptive attacks.
11. The Lance Formation (Central Echelon). You basically have order 3 but with an even faster center to compensate for the lack of direct reinforcement by line. Three Landraider Inquisition forces, Orks with Bikers instead of Choppers and the like use this regularly. Your faster force hits the middle and divides the opposition with a breakthrough. Your stronger but slower stuff hits the sides and you win. Counter as you would 4.
12. Columns. The height of Jomini era thinking. Sadly it doesn't translate well to 40k. Too much of your force ends up as a mobile reserve and you either win or loose on the strength of the front of your columns. I've included it mostly for completeness.
So there you are. I personally don't think there are any formations of deployment and attack that I've seen in 40k that Jomini didn't cover, smart guy I bet he didn't play Marines - probably Guard of some sort. The best part is now that you've seen all the options and know what they do and what to do to them you can respond better. Yey Anticipated Friction.
James