Reading the "Vietnam Primer" the section on company wedge formations particularly struck me. The relevant passage is reproduced here. The diagrams are not that helpful. Some give the impressions that the company has five or more platoons, and it is not clear what formation the platoons and squads are in.
According to FM 7-10 the infantry company may move in Line, Column, File, Wedge, Vee, Echelon Left and Echelon Right formations.
I've never handled a company, but to me it seems for movement outside combat you only need three formations- the File, for when there are terrain restrictions; the Column, for movement at speed and the Double Column for movement where enemy activity is suspected.
For the Double Column each column is headed by one rifle platoon in Wedge (Arrowhead) formation. The rest of each column may be in Platoon Column or Platoon Wedge. The third rifle platoon forms the tail of each column and the weapons and HQ elements form the centres of the columns. One mortar team travels with each column and one column is commanded by the company commander, the other by his 2inC.
Space between the columns should equal column length when possible, so effectively the formation occupies a square. Movement in Double Column is easy since it is essentially just two short columns that are just kept approximately level.
On encountering an enemy ahead of the formation the lead platoons are already in Platoon Wedge, so have good all around firepower. From this formation they can both form a line, or alternately move into Platoon Vee formation as the lead squad "rolls with the punch" of contact and regroups to form the rear squad. While the lead platoons engage the rear platoons have the option of either strengthening or extending the line or acting as a reserve and laying down mortar fire.
If attacked from the flank the column is essentially already in a line. The other column can act as a reserve or reinforce the other column.
There may be applications for other company formations once combat is joined, but for movement the File, Column and Double Column have the virtue of simplicity and ease of control and will meet most needs.
Veteran tanker and famous author Ralph Zumbro has made me aware of another Company formation very useful for mechanised forces:- the line of platoons in column. In other words, three columns of vehicles moving parallel to each other. Many of the tank companies Ralph served in contained 17 tanks, so each column would be of five vehicles. The CO's and XO's tank would take position between the leading tanks of each platoon, so in effect the formation formed a square five tanks wide and five to each side. Ralph notes that the formation could easily move into an arrowhead formation at a moments notice. Similar formations can be used by companies with three or four platoons of four vehicles.