What is the English term for "assume the least dangerous body pose when falling"?

The tuck position

  • resembles a ball with the knees bent and the legs pulled as close to the body as possible. Each hand should grasp the leg on the shin, midway between the knee and the ankle. The toes should be pointed and the legs kept together as the diver goes off the board.

(Encyclopedia Britannica)

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The term comes from diving:

tuck:

  • As a folded-up diving position, from 1951.