E and D

According to the source below,

E is a 1-form. Not a vector! (According to other reputable sources, the 2-form in full Minkowski spacetime is a better representation.)

D is a 2-form.

(BUT, according to https://physics.stackexchange.com/questions/86510/maxwells-equations-using-differential-forms they are both 2 forms in 4d spacetime.)

$\star$dx=dydz

$\star$dy=dzdx

$\star$dz=dxdy

And

D= $e_0$ $\star$E

"The surfaces of E are perpendicular to the tubes of D"

And

"The star operator relates 1-form surfaces to perpendicular 2-form tubes."

And

"...the star operator depends on a metric. If the metric is related to the permittivity or the permeability tensor, anisotropic star operators are obtained, and the constitutive relations become D= $\star_a$ E. Graphically, an anisotropic star operator acts on 1-form surfaces to produce 2-form tubes that intersect the surfaces obliquely rather than orthogonally."

https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=1668&context=facpub

Note:

https://en.wikipedia.org/wiki/Metric_tensor_(general_relativity)#Volume

And

https://en.wikipedia.org/wiki/Hodge_star_operator#Computation_in_index_notation