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quadrupedalism

n. The condition of being a quadruped.

Wikipedia
Quadrupedalism

Quadrupedalism or pronograde posture is a form of terrestrial locomotion in animals using four limbs or legs. An animal or machine that usually moves in a quadrupedal manner is known as a quadruped, meaning "four feet" (from the Latin quattuor for "four" and pes for "foot"). The majority of quadrupeds are vertebrate animals, including mammals such as cattle, dogs and cats, and reptiles, like lizards.

Most other species are usually not quadrupeds, with some exceptions; for example, among the insects, the praying mantis is a partial quadruped. A few birds may use quadrupedal movement in some circumstances; for example, the shoebill will sometimes use its wings to right itself after lunging at prey.