Up until the early 20th century a strong, solid formation had been the fundament of massed infantry tactics. A solid formation allowed you to concentrate your combat fire. When bows and later firearms became established as major infantry weapons the formation let you concentrate your firepower. Importantly, a solid formation gave the infantry some protection against shock action by cavalry. These benefits were not without a price, however. A large formation was a large target for artillery and missile fire. (originally “Artillery” was a term used for slingers and bowmen). By the start of World War One infantry firearms had reached a level at which cavalry attacks against ready infantry were no longer practical. With this threat removed the need for infantrymen to fight shoulder to shoulder was also removed, and troops could disperse to make themselves harder targets. This is not to say that selection of formation does not have a part to play in modern military operations. The role of formations now is to facilitate the concentration of firepower, mutual support and response to threats. When cavalry were a threat keeping the Line or square unbroken was critical. For a modern unit creating a perfect geometric shape is not the objective of the exercise. A Platoon arranged in a perfect Line is very vulnerable to flanking fire or strafing by aircraft. If the Line is a bit ragged the elements are less vulnerable but can still concentrate their fire as effectively.
This page is a brief primer on Team, Squad and Platoon tactics and formations. These are sites on the web that have helped my understanding.
The Team formations are basically the same thing as the SAS four man patrols, but with one striking difference. SAS does not have the leader as the point man. Usually he will be the second man in the formation. The third man will usually be the signaler and the tail-end charlie will be the second in command.
I'll also mention here that there are other formations for a Team other than File | and Wedge. ^ There is also Box formation,  essentially two files, and useful for moving down features such as roads since it gives equal firepower to all directions. There is Diamond formation, ¨ very similar to Wedge formation. It has slightly less immediate frontal firepower but the rear man can move more readily to either flank. When a Diamond halts each man looks to a point of the compass for all around observation. Diamond formation is a good formation to adopt any time a Team halts. There is also echelon left and right:- basically / or \ a diagonal file or line at about 45° to the direction of travel. This offers a good field of fire forward and to one side. Useful when another team or terrain feature protects the other flank. Last of all there is the Line ____ which gives maximal firepower to one direction. You'll see that all of the above formations can easily move into a line by just a couple of men moving forward or moving back.
There is a variation of squad arrowhead formation used when a patrol is tracking. The point and each tip of the arrowhead is formed by two men, one tracking, the other providing security overwatch. In the centre of the arrowhead is the Squad Leader and the RATELO. See FM 21-75 Appendix E, Tracking.
When a platoon is mounted on four vehicles the formations used are similar to those used by a four man fireteam. The line is used for maximum frontal fire. Echelon is formed by one or more vehicles dropping back. If the middle pair of vehicles in a line drop back a V is formed, while the vehicles on the end dropping back forms a Wedge. Column or Staggered Column (a variant of Box) is used for moving where there is insufficient room to spread out. "Herringbone" is used when a column halts, while Coil is stationary Diamond formation.
Here I'll add an interesting set of observations by Ralph Zumbro.
One of the oddball things we discovered in RVN was that if you add a few left-handers to your point squad, it has a better chance of surviving an ambush because they habitually carry their weapons pointed to the right. Also a non smoking point man can SMELL fish-eaters....And somone who is color blind compensates by seeing more texture and can usually spot camouflage, especially day old dead foliage.
In fact the best description of Platoon formations that I have come across are on the following pages for the game Combat Mission.
Since these pages now appear to be off-line I'll reproduce some of the text with a few additions:-
The Platoons described consist of three rifle squads and a Command section. Most modern platoons also include a Weapons squad, but this can be taken to be moving with the Command section, so where "Command Section" is written this can be read as meaning Weapons Squad and Command Section.
BASIC PLATOON FORMATIONS There are four very basic formations which are mentioned in virtually any military handbook The Line The Vee The Wedge and The Column
These four represent the basic knowledge a platoon commander should have with regard to a coordinated use of his infantry combat assets. All four have their advantages and disadvantages, and a sound understanding of these is going to be a great aid in winning tactical battles in Combat Mission - or a real war for that matter: -
THE LINE FORMATION The most basic of all formations puts all three squads of a platoon in a straight line abreast of each other, with the platoon leader providing command & control from a position slightly to the rear. . This is an all-out assault position, concentrating maximum firepower to the front of the platoon, but neglecting the flanks. It therefore should only be used when the location of the enemy is known (to the front) and/or when adjacent friendly units are capable of securing the flanks of the platoon. By attacking from the flanks, the enemy otherwise would be able to bring his entire assaulting formation to bear on each squad pretty much one at a time, thereby rolling it up from the side with little difficulty. The line formation is mostly used when the platoon is tasked with providing suppressive fire onto a certain enemy location from within an extended friendly line (as preparation for and/or during an assault), but it can also be used as a "human wave" attack on a known (and hopefully suppressed) enemy location (the latter use is specifically mentioned in George Forty's "DS Army Handbook 1939-1945", page 174 "Assault Doctrine" ).
THE VEE FORMATION (Sometimes called The Fork. Tines go towards the enemy).This is essentially a slight variation of the line formation discussed above. It is achieved by pulling the middle squad back from the front line. This entails a slight weakening of the firepower to the front, but provides the platoon leader with a maneuver element to be used in an unexpected enemy flanking assault. In such instance, the middle squad can be used to reinforce each flank by quickly moving in behind one of the forward units and use direct fire from an alternative position on any assaulting enemy. But even if such a move is not possible (e.g. because the counterattack has been a complete surprise), its mere location away from the front line will enable the middle squad to provide suppressive fire into the counterattacking enemy's flank, thereby either stalling this effort completely or at least covering the retreat of the other forward elements. The Vee formation is a slightly more defensive formation than the line, which features a good balance of offensive firepower to the front and enhanced security against enemy flanking attacks. It is used mostly in otherwise unsupported fighting positions where the location of the enemy is known or strongly suspected, or in supported positions with a suspected enemy on one or both flanks. (A variation of this shown in modern US Army manuals is to place the rear rifle squad behind the command section to create a local reserve that can maneuver to reinforce either flank.)
THE WEDGE FORMATION The most defensive of the three formations based on the line, the wedge formation sacrifices frontal firepower for maximum flank security. It is achieved by pulling the right and left squads back out of the line, thereby presenting always two squads towards any flanking enemy attack. The wedge (sometimes also referred to as Diamond) formation is therefore mostly used when the enemy location is unknown and/or the platoon is in an unsupported position without adjacent friendly units on either or both flanks. It is also a decent formation for a cautious advance into unknown enemy territory - should the point squad come under attack/ambush, a defensive line formation can be quickly established to the front by pulling the point squad back into the line, while the two rear squads provide covering fire on known or suspected enemy locations and are able to prevent the enemy from pursuing the point squad. (Current US Army manuals show the command section and weapons squad in the middle of the triangle formed by the three rifle squads.)
THE COLUMN FORMATION The column formation is essentially not a combat formation. It is mostly used during advances when contact with the enemy is highly unlikely. It allows the use of roads or narrow paths for the entire formation, avoids slowdowns during the advance (when one squad has to move through thick forest while another travels on a clear field) but still provides minimum security for all platoon elements by assigning each squad a unique task within the formation:
Point squad (scouting ahead for possible enemy locations and mines),
Supporting squad (providing fire support if point squad achieves contact with enemy)
Platoon HQ (in a position to provide command & control to all platoon units)
Rear point (covering the rear of the column and providing security for the platoon HQ)
In case of enemy contact, the column formation can be deployed offensively or defensively with minimum effort by either:-
- moving the rear point forward beside the point squad, while the supporting squad moves to the other flank,
- pulling back the point squad beside the supporting squad, while the rear guard moves up,
- pulling the supporting squad back beside the rear point in case of an attack from the rear.
The use of the column formation should be limited to the opening stages of a battle in Combat Mission and within friendly lines, and the platoon should be deployed into a combat formation as soon as contact with the enemy is probable (even if not likely).
Common Variations One Forward This is basically the line formation with a fire-team from the middle squad place well forward to scout. The remaining whole squads are placed left and right of the scouting point and are thus able to flank any enemy position to the front and/or provide a firm fire line ("base of fire") to enable the forward half-squad to withdraw. This formation is good for relatively open terrain where the point team is able to oversee an area as wide as the platoon's base of advance (essentially three squads wide): otherwise the danger of the scouts to miss and enemy position left and right might result in the trailing squads stumbling right into their field of fire. (Being a line formation this is weak on the flanks. Conceivably a wedge could be used with a team forward.)
Two Forward or Two on the Flanks Two Forward is essentially a diamond formation with the lead squad split into two teams and advancing in a line slightly wider than the front of the trailing squads. This is a better formation for restricted terrain since the two scout teams cover the whole width of the platoon's advance. The formation is also better when an enemy is likely to be encountered on the flanks since an enemy will encounter the fire of at least a squad and a half. This formation is also used for a pincer assault against an objective with the two rear squads providing support fire while two teams attack from different directions.
Two Scouts This is the Vee formation with both the forward squads split into scout teams. The advantage of this is that it gives very through scouting and presents more than one target to an enemy encountered. The half-squads can also support each other. The rear squad and command section can support the scouts and act as a rallying point. Main disadvantage is that forward combat power is spread thinly should a quick assault against an encountered enemy be required.
Scouting Platoon Column. (I tend to think of this as the Centipede formation since it has a long body with two feelers.) This is the column described above with the lead squad split into two teams that advance to either side of the column. These teams are staggered slightly so they do not both encounter an ambush at the same time and can provide covering fire to each other. This formation increases the security of a column while still allowing it move rapidly. A variation is to place one team at the front and one to the side of the command section. This team increases flank security but can also move to reinforce the rear squad. On contacting an enemy ahead the lead team withdraws and the other squads move into a more aggressive formation.
To this list of formations we can also add the Platoon File shown in the Manual. All of the Platoon are in single file other than a Team in Wedge at the point and a Team Wedge either side for flank security.
As a rule of thumb a Platoon attacks as either a Line or a Vee, depending on the risk to the flanks. It moves as a Column when speed is priority and a Wedge if enemy contact is expected. Teams within the Platoon move as Wedges and Squads move as Columns unless attacking.
The Column formation allows a unit to move rapidly, is easy to control and has good flank security. The small frontage presents less of a target to enemies and reduces vulnerability to booby-traps and mines. Disadvantage of this formation is that it can only apply a small part of its combat power to the front until it redeploys. On another page an argument is made for the use of the Double Column as a movement formation for Companies. The Double Column or Staggered Column may also have applications for dismounted Platoon movement - Staggered Column is already recommended for moving when mounted. An enemy encountering a Platoon in such a formation will always be confronted by at least two Squads and those Squads not engaged can easily maneuver into Line or Vee formation or flank the enemy.
Four Rifle Team Platoon. An article by William Owen suggests a platoon that consists of a machine gun team, HQ element and four five-man squads (which he terms Fire Teams). Some mention is worth making of how such a unit would use the formations described above.
Line. Four rifle squads abreast. Command section and MG team postioned behind. Vee. Two teams form each arm of the V with the command and weapons team as the bottom point. Wedge. Two teams at the front in line, one team on each side further back and further out. Command team at the rear. Resembles a diamond with the forward point cut off, or a stylized letter M. Resembles the wedge formation used with a four vehicle platoon with the command team trailing or in the middle. Column -as before. The Centipede formation can be formed with one five man rifle squad for each antenna rather than a half-squad.
Quick Summary Most common Team formation for movement is a Wedge, though others are possible and in certain situations more useful. Upon contact a Team usually forms a Line to maximise firepower. Most common travelling formation for a Squad is to move in Column with the Teams in Wedges. Best travel formation for a Platoon is the Wedge, with Squads in Column and their Teams in Wedges. Terrain features or the need for speed may place a Platoon in Column or File. Platoon Lines or Vees are used when contact has been made or is about to be made with the enemy.
On the topic of communications, in his book The Jungle is Neutral Spencer Chapman relates on how they broke down their communications to just two noises. A single click of the tongue meant Stop or Danger, two clicks of the tongue meant Go on or OK. Rallying call was the call of a non-indigenous bird (a barn owl I think). The same level of communication could be made with just two hand signals. Raised palm for one click, waving forward with the hand lowered for two clicks.