This is a subtype of the HodgeSpecialFourfold type.
The object IntersectionOfThreeQuadricsInP7 is a type, with ancestor classes HodgeSpecialFourfold < EmbeddedProjectiveVariety < MultiprojectiveVariety < MutableHashTable < HashTable < Thing.
The source of this document is in /__w/M2/M2/macaulay2-1.26.05+ds/M2/Macaulay2/packages/SpecialFanoFourfolds/docs.m2:508:0.