Reading the intro chapters to my Griffiths electrodynamics, I ended up re-deriving the 1,2 and 3 parameter variations of Stokes Theorem (a quick derivation as previously done using Geometric Algebra [PDF], but without looking at my notes). To understand how to map from the algebraic representation to a geometric one for the 3 parameter volume element, I built the following nice little model:

This is like Fig 1.10 from the pdf notes linked above, but was a lot more fun to construct than the drawing.