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Vyuhas or' Strategic Formations'
Makara Vyuha (Crocodile formation): 

On the fifth day of the war, Bhishma chose to arrange his army in Makara Vyuha. Arjuna, Yudhishthira, and Dhristyadhumna decided for the Hawk formation of their Army. All the warriors of both sides were assigned to specific places in the formations with special responsibilities.

On the sixth day, it was the Pandavas who preferred the Makara Vyuha. The Kauravas chose Krauncha Vyuha. On this day Bhima was coming in and out of the Vyuha of the Kauravas, killing soldier at will, swinging his terrible mace.

Krauncha Vyuha (Heron formation)

Krauncha Vyuha was usually met with Garuda or eagle Formation/ ’Eagle is a Natural Enemy of Heron. Note the Swoop of the Garuda, nullifying and swamping the posture of the Heron. In its form, the Garuda Vyuha resembles the Krauncha Vyuha, with a subtle difference that it resembles an eagle. On the second day, Bhishma arranged his army in Garuda Vyuha to counter the Krauncha Vyuha of the Pandavas. Bhishma himself got positioned at its beak. Drona and Kritavarma were the eyes. Kripa and Ashwatthama were at the head. The Trigartas the Jayadratha with their armies made the neck. Duryodhana, his brothers, Vinda and Anuvinda made the body of the formation whereas the King of Kashala, Brihadbala formed the tail of the formation.

This military formation on a pattern is supposed to resemble a heron with outstretched beak and spreading wings. Krauncha Vyuha, a very offensive formation, was generally attempted to induce fear in the opponent army. Pandava army was arranged in this Vyuha on the second day of the Mahabharata war. Drupada was at the head and Kuntibhoja was placed at the eye. The army of the Satyaki formed the neck of the Krauncha bird. Bhima and Dhristyadhumna formed both the wings of the Vyuha. The sons of Draupadi and Satyaki were to guard the wings. The formation of the army phalanxes in this manner was very formidable. The Krauncha Vyuha was also arranged by Bhishma. Bhurishrava and Shalya were to guard the wings. Somdatta, Ashwatthama, Kripa, and Kritavarma were positioned at a different important place in the formation.

Mandala Vyuha (Galaxy formation)

It was a defensive circular formation very difficult to penetrate. The Commander-in-chief, situated at the center of the formation, usually leads the army and is surrounded by several small groups of army men, each group lead by a Maharathi. On the seventh day of the war, Bhishma made Mandala Vyuha. The Pandavas countered it by Vajra Vyuha.

Vajra Vyuha (Diamond or Thunderbolt Formation)

Pandavas chose Vajra Vyuha to counter Mandala Vyuha formation on the 7th day. This formation was also used by the Pandavas on the first day of the war. In this formation, all Maharathis is situated at the center of the squared formation and are surrounded by infantry from all sides. Drishtadhyumna lead the formation and was followed by the five Pandavas on the 7th day. And it was Bhima who lead the formation on the first day.

Ardha Chandra Vyuha (Half crescent formation)

Arjuna arranged this formation in consultation with the commander of the Pandava army Dhristyadhumna on the 12th day of the war his arrangement. At the right end was the powerful Bhima. Abhimanyu was at the left end. Ghatotkacha and Kokaya brothers were at the left rear. Satyaki and five sons of Draupadi were at the rear center. Yudhishthira was placed at the center of the formation. The armies of Drupada and Virata led from the front guarding Yudhishthira. Neel and Dhristyadhumna were placed next to them with Dhrishaketu and Shikandi following at the rear end. At the tip was Arjuna at his Chariot with Krishna.

Shakata Vyuha (Box or Cart formation)

Shakita Vyuha is an array in which the army is drawn up in a narrow and compact order and it is rear expanding in extended columns like the back of an Indian cart. Drona used this formation on the 11th day for the Kauravas.

Sarvatomukhi Dand Vyuha 

This was the formation used by Bhishma on the 1st day of the Kurukshetra war. The head of the formation had 6 Maharathis arranged in a circular form and the rear end is shaped like a rod (Dand) to keep resourcing the head.