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Calyrex is a bipedal, mammalian Pokémon. Its main body is light gray with a round torso and long, white legs with no visible digits. It has four long ears with white tips that hold up its large brain, which is green with a light purple top. Around its neck are smaller features similar to its brain around its neck like a necklace, with the smallest one in the front and the largest one in the back. Its arms are short with white tips and no visible digits. Its long face has a white underside, half-closed purple eyes, and a black triangular nose. It also has four purple insect-like wings which may give off the impression of a royal cape.
Calyrex is said to have ruled Galar in ancient times. Despite its delicate and slight appearance, it can move with grace and dignity. It is known to be highly intelligent. It also has the power to see the past, present, and future of any kind.
Calyrex may be based on an arctic hare and a crown. The large bulbs on its head resemble berries or flowers. It also bears some resemblance to fictional taxidermy creations, such as the American jackalope or the German wolpertinger. Its beads around its neck each bear the Hōjō clan symbol.
Calyrex may be a combination of calyx (Latin for bud) and rex (Latin for king).
Budrex may be a combination of bud and rex (Latin for king).