Pokémon Forms
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"Pokémon forms" is typically used to refer to gendered forms, although some Pokémon (such as Castform) may have alternate forms they can switch between in dungeons.
Gender Forms
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There are four possible gender settings: Male, Female, Genderless, and Invalid.
In vanilla Explorers of Sky, if a Pokémon only appears as one gender form, its first gender form will be listed as the desired single gender (Male, Female, or Genderless), and its second gender form will be listed as Invalid.
Special Pokémon Forms
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Certain Pokémon have specific forms they switch between depending on certain conditions. Other Pokémon have more forms than just the two gender slots.
Pokémon that change form in dungeons are hardcoded to have all of their forms' sprites loaded at once, which makes their sprite size and body size surprisingly large.
Unown
Unown is a special case in this list because it has some hardcoded behavior relating to its name.
Castform
Deoxys
Cherrim
Giratina
Giratina changes from Altered Forme to Origin Forme in Explorers of Sky-exclusive dungeons. Giratina's Altered Forme is hardcoded to receive a +2 stage boost to its Defense and Special Defense, and a -2 stage reduction to its Attack and Special Attack. Giratina's Origin Forme has this reversed; it instead receives a +2 stage boost to its Attack and Special Attack, but a -2 stage reduction to its Defense and Special Defense.
In the Japanese version only, this behavior is affected by a significant bug; the Defense and Special Defense stage modifications are applied to the opponent Giratina faces rather than Giratina itself.
Shaymin
Shaymin changes from Land Forme to Sky Forme upon using a Gracidea. It is hardcoded to have double movement speed in Sky Forme.
Note that the Gracidea item does not work until you clear Sky Peak.