Final answer:
The cranium or skull is the structure that encompasses the brain in vertebrates, protecting it while also supporting the face.
Step-by-step explanation:
The structure that encompasses the brain in vertebrates is called the cranium or skull. The cranium is a bony, cartilaginous, or fibrous structure that supports the face and protects the brain. It is subdivided into the facial bones and the brain case, or cranial vault.