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Since divya has been banned, I think I will hijack this thread
The formations I will discuss are NOT, however, mythological. Rather, they are actual formations used by ancient Indian armies during the Maurya Empire, as described by Chanakya in his masterpiece Arthashastra.
Chanakya describes four basic varieties of formations:
1. Danda - the staff-like array
2. Bhoga - the snake-like array
3. Mandala - the circle-like array
4. Asamhata - the detached order
Each of these four varieties, in turn, has its own variations. I will try to describe as many of these variations as possible, using direct information from the Arthashastra.
I will also provide illustrations to better depict these formations. All images are my own work (hence the low-quality, LOL)
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First, let us discuss the danda, or "staff-like array". According to Chankaya, this is a formation in which all the constituents of the army stand abreast. This would make it the most simple type of array.
The pradara is a variant of the danda. The purpose of this formation is to break the enemy's formation. To achieve this, the flanks are made to project forward, and generally consist of "shock" units such as war elephants, heavy chariots, and armored cavalry.
The pradara can be countered by means of the dridhaka.
The dridhaka (which means "firm") is a defensive variant of the danda, and is meant as a counter to the pradara. The flanks and wings are stretched back, and are designed to absorb the blow of a frontal attack. The dridhaka typically consists of sturdy mail- and plate-armored infantry.
The dridhaka can be countered by the asayha.
The next variant is the "irresistible" formation, or asayha. It conists of elongated wings designed to envelop the enemy. The wings usually conist of fast and maneuverable units like light and medium cavalry (and sometimes chariots or elephants). It is most useful against compact formations like the dridhaka.
The asayha can be countered by means of the Syena vyuha.
The Syena vyuha ("eagle formation") of Mahabharat lore can be dscribed as a variant of the danda as well as the asayha. The Syena vyuha consists of a projected front in addition to elongated wings. It is designed for a "comprehensive attack" by all constituents of the army; it can shatter the enemy's center while simultaneously conducting an enveloping attack on its flanks and rear. As with the asayha, it is most useful against compact formations.
The Syena vyuha can be countered by means of the sanjaya formation.
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I will post more formations and their details when I have time. Comments are highly appreciated.
Excellent post.
I will mention that all variations you mentioned, seem to me are closely related or derived from the Phalanx of Philips or Alexander of Macedon.
A vyuha can't be considered static, and all the variations you mentioned are infact movement under certain circumstances and strategy.