Square division

In a square organization, the division's main body is composed of four "maneuver," i.e., infantry regimental elements.

The usual internal organization within a square division would be two brigades, each comprising two infantry regiments (consisting of two or three battalions.)

By contrast, a triangular division generally has its infantry units organized in a "three by three" format.

(In many armies, more recently, the infantry regiment, as a combat formation, has been abolished and triangular divisions are made up of three brigades, each consisting of three battalions.)

Recent reforms in the United States and several European countries have placed greater emphasis on the brigade as the major tactical formation, with the division now acting more like a corps headquarters, controlling several relatively autonomous brigades and parceling out support units based on the tactical situation.

Square division example: 1940 U.S. infantry division. On the far left can be seen two brigades of two regiments each
Triangular division example: 1942 U.S. infantry division. The brigades of the square division have been removed, and there are three regiments directly under divisional control.