The Hodge star works like this:
i1 : ea = exteriorExtension(3, 6, e, QQ);
i2 : ea.HodgeStar(first ea.bases#1) o2 = e e e 3 4 5 o2 : QQ[e ..e ] 0 5
This is the exterior algebra. HodgeStar of a module is the Hodge dual.
The object HodgeStar is a symbol.
The source of this document is in ExteriorExtensions.m2:681:0.