An object of the class HodgeSpecialFourfold is basically represented by a couple (S,X), where $X$ is a fourfold and $S$ is a surface contained in $X$. Such objects are created by the function specialFourfold.

- specialFourfold -- make a Hodge-special fourfold
- SpecialCubicFourfold -- the class of all special cubic fourfolds
- SpecialGushelMukaiFourfold -- the class of all special Gushel-Mukai fourfolds
- IntersectionOfThreeQuadricsInP7 -- the class of all special intersection of three quadrics in P^7

- IntersectionOfThreeQuadricsInP7 -- the class of all special intersection of three quadrics in P^7
- SpecialCubicFourfold -- the class of all special cubic fourfolds
- SpecialGushelMukaiFourfold -- the class of all special Gushel-Mukai fourfolds

- mirrorFourfold -- associated fourfold to a rational cubic or GM fourfold
- specialFourfold -- make a Hodge-special fourfold

- ambientFivefold(HodgeSpecialFourfold) -- see ambientFivefold -- get the ambient fivefold of the Hodge-special fourfold
- clean(HodgeSpecialFourfold) -- clean the internal information of a fourfold
- detectCongruence(HodgeSpecialFourfold) -- see detectCongruence -- detect and return a congruence of secant curves to a surface
- detectCongruence(HodgeSpecialFourfold,ZZ) -- see detectCongruence -- detect and return a congruence of secant curves to a surface
- discriminant(HodgeSpecialFourfold) -- see discriminant(SpecialCubicFourfold) -- discriminant of a special cubic fourfold
- mirrorFourfold(HodgeSpecialFourfold) -- see mirrorFourfold -- associated fourfold to a rational cubic or GM fourfold
- parameterCount(HodgeSpecialFourfold) -- see parameterCount -- count of parameters
- parametrize(HodgeSpecialFourfold) -- rational parametrization
- surface(HodgeSpecialFourfold) -- see surface -- get the special surface contained in the fourfold
- toExternalString(HodgeSpecialFourfold) -- convert to a readable string
- unirationalParametrization(HodgeSpecialFourfold) -- see unirationalParametrization -- unirational parametrization

The object HodgeSpecialFourfold is a type, with ancestor classes EmbeddedProjectiveVariety < MultiprojectiveVariety < MutableHashTable < HashTable < Thing.