What are some famous military formations and strategies used in Mahabharata war at Kurukshetra?

Question

What are some military formations and strategies used in Mahabharata war at Kurukshetra?

I heard Padma Vyuha was a famous one, From wikipedia

Padmavyūha, is a multi-tier defensive formation that looks like a blooming lotus (padma, पद्म) when viewed from above. Very famous because of the warriors at each interleaving position would be in an increasingly tough position to fight".

Who were the warriors capable of fighting in Padma Vyuha?

Answer 1

I have found an interesting list of all the strategies used in the twelve days of battle. Usually, one side chose a specific strategy at the start of the day, to which the other side reacted by choosing their counter-strategy.

1. Chakra vyuha – formation of concentric circles in layers.
2. Shakata vyuha – formation of a cart wheel
3. Mandala vyuha – circular formation ( don't know how this is different from the above)
4. Urmi vuyha – formation resembling ocean’s waves
5. Sarvatobhadra vyuha – meaning “safe on all sides” – seems to have been a kind of square array in which the troops faced all the points of the compass (as per KMG interpretation)
6. Garuda vyuha (Garuda – The Mighty Bird).
7. Krauncha vyuha ( Krauncha is bird with a sharp pointed beak)
8. Vajra vyuha ( in the shape of the thunderbolt)
9. Suchimukha vyuha ( formation in the shape of a needle)
10. Padma vyuha (formation of a blooming lotus)
11. Sura & Asura vyuha hv been mentioned as well (cant interpret how they were)
12. ArdhaChandraakara vyuha (crescent shape)
13. Makara vyuha ( crocodile-shaped)

From: Military Formations in Mahabharata

Answer 2

1st Day:

Kauravas – Bhishma Pitamah – “सर्वतोमुखी दण्डव्‍यूह”(“Sarvatomukhi Dand Vyuha”) Pandavas – Arjuna -“वज्र व्यूह”(“Vajra Vyuha”)

2nd Day

Kauravas- Bheesma -“गरुड़-व्यूह” (“Garuda Vyuha”) Pandavas- Dhristyadhumna -“क्रौंच व्यूह” (“Krounch Vyuha”)

3rd Day

Kauravas – Bheesma – “गरुड़-व्यूह”(“Garuda Vyuha”) Pandavas – Arjuna – “अर्धचन्द्र व्यूह” (“Ardhchandra Vyuha”)

4th Day

Kauravas – Bheeshma – “मंडल व्यूह” (“Mandal Vayuha”) Pandavas – Arjuna – “श्रीन्गातका व्यूह” (“Sringataka Vyuha”)

5th Day

Kauravas – Bheeshma – “मकर व्यूह” (“Makar Vyuha) Pandavas – Arjuna – “श्येन व्यूह”(“Shyen Vyuha”)

6th Day

Kauravas – Bheeshma – “क्रौंच व्यूह” (“Krounch Vyuha”) Pandavas – Dhrishtadyumna – “मकर व्यूह” (“Makar Vyuha”)

7th Day

Kauravas – Bheeshma – “मंडल व्यूह” (“Mandala Vyuha”) Pandavas – Arjuna – “वज्र व्यूह” (“Vajra Vyuha”)

8th Day

Kauravas – Bheeshma – “कुर्मा व्यूह” (“Kurma Vayuha”) Pandavas – Arjuna – “त्रिशूल व्यूह” (“Trishulq Vayuha”)

9th Day

Kauravas – Bheeshma- “सर्वतोभद्र व्यूह” (“Sarvatobhadra Vyuha”) Pandavas – Arjuna – “नक्षत्र मण्डल व्यूह” (“Nakshatra Mandal Vyuha”)

10th Day:

Kauravas – Bheeshma – “असुर व्यूह” (“Asura Vyuha”) Pandavas – Arjuna- “देव व्यूह” (“Dev Vayuha”)

11th Day:

Kauravas – Drona – “शकट व्यूह” (“Shakata Vyuha”) Pandavas – Arjuna – “क्रौंच व्यूह”( “Krouncha Vyuha”)

12th Day:

Kauravas – Drona – “गरुड़ व्यूह” (“Garuda Vyuha”) Pandavas – Arjuna – “अर्धचन्द्र व्यूह” (“Ardhachandra Vyuha”)

13th Day:

Kauravas – Drona – “चक्र व्यूह” (“Chakravyuha”) Pandavas – Abhimanyu – No Vyuha was formed on this day because Abhimanyu was the only warrior that entered Enemy’s formation while rest of the army was held back on gate 1.

14th Day:

Kauravas – Drona – “चक्रशकट व्यूह”, (“Chakrashatak Vayuha) Pandavas – Arjuna – “खड्ग सर्प व्यूह” (“Khadag Sarpa Vyuha”)

15th Day:

Kauravas – Drona – “पद्म व्यूह”(“Padma Vyuha”) Pandavas – Arjuna – “वज्र व्यूह” (“Vajra Vyuha”)

16th Day:

Kauravas – Karna – “मकर व्यूह” (“Makar Vyuha”) Pandavas – Arjuna – “अर्धचन्द्र व्यूह”(“Ardhachandra Vyuha”)

17th Day:

Kauravas – Karna- “सूर्य व्यूह” (“Surya Vyuha”) Pandavas – Arjuna – “महिष व्यूह” (“Mahish Vyuha”)

18th Day:

Kauravas – Shalya – “सर्वतोभद्रव्यूह”(“Sarvatobhadra Vyuha”) Pandavas – Arjuna – “क्रौंच व्यूह”( “Krounch Vyuha”)

http://www.lonelyphilosopher.com/ranks-and-hierarchies-of-soldiers-in-mahabharata-war/

Answer 3

A vyuha was formed by Kauravas to protect Bhishma from Shikhandini which is known as Sarvatobhadra.

BORI CE by Bibek Debroy, Chapter 955 (page 2623)