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What is Quad Helix is: and explain in detail?
Indications of quad helix appliance: 

Narrow upper arch that needs expansion, e.g., in cross-bites.
Crowded mixed or permanent dentition in which long-range growth can be predicted and requires mild expansion as there is lack of space for the upper laterals.
Class II malocclusions where upper arch needs effective widening and upper molars need distal rotation.
Class III malocclusions where upper arch needs effective widening and advances with class III elastics.
Thumb sucking and tongue thrusting cases with its modifications.
Unilateral or bilateral cleft palate. 

Textbook of ORTHODONTICS Sridhar Premkumar