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What are the three major forms of insect pupae?

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Illustration showing a variety of adult insects, each labeled with its common name and order, including walkingstick, earwig, stonefly, tree cricket, dragonfly, female scale, cat flea, thrips, sucking louse, thysanuran, ant, scarab beetle, stinkbug, mosquito, and cabbage butterfly, highlighting their diverse shapes and sizes. — insect An illustration of insect diversity.

In the study of insects that undergo complete metamorphosis, the pupa stage is categorized into three primary forms based on the arrangement of the insect's appendages and its protective covering:

Exarate: The appendages (such as legs and antennae) are free and not attached to the pupal skin.1
Obtect: The appendages are tightly fastened or glued to the body wall, often resulting in an immobile pupa.12
Coarctate: The pupa develops within the hardened, shed exoskeleton of the final larval stage, which serves as a protective covering.13