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.
The object HodgeSpecialFourfold is a type, with ancestor classes EmbeddedProjectiveVariety < MultiprojectiveVariety < MutableHashTable < HashTable < Thing.
The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/SpecialFanoFourfolds.m2:3641:0.