The Tortoise
Repel
Calvary The order to repel cavalry brought about a the following formation. The first rank would form a firm wall with their shields, only their pila/throwing spear protruding, forming a vicious line of glistening spearheads ahead of the wall of shields. A horse, however well trained, could hardly be brought to break through such a barrier. The second rank of the infantry would then use its spears to drive off any attackers whose horses came to a halt.
The Orb
The orb is a defensive position in the shape of a circle taken by a unit in desperate straits. It allows for a reasonably effective defence even if parts of an army have been divided in battle and would have required a very high level discipline by the individual soldiers.
Skirmishing Formation
The skirmishing formation was a widely spaced line up of troops, as opposed to the tighter packed battle ranks so typical of legionary tactics. It allowed for greater mobility and would have found many uses in the tactical handbooks of Roman generals.
The wedge
The
wedge was commonly used by attacking legionaries, - legionaries formed up in a triangle, the front 'tip' being one man and pointing toward the enemy, - this enabled small groups to be thrust well into the enemy and, when these formations expanded, the enemy troops were pushed into restricted positions, making hand-to-hand fighting difficult. This is where the short legionary
gladius was useful, held low and used as a thrusting weapon, while the longer Celtic and Germanic swords became impossible to wield.