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The faces of a bivector can be indistinguishable. They can be transparent.
All we need is a sense of circulation around the edge.
As a super-important example, the volume of a parallelepiped is given
by the trivector A∧B∧C which is equal to A×B·C ... definitely not A×B×C.
This misses a vitally important piece of information. Trivector A^B^C
is more than just volume (and shape) of the respective
parallelepiped. It also decrees the way we go around the
parallelepiped along its edges.
In fact, this piece is explicitly formulated in the following (correct!) statement about bivectors:
All we need is a sense of circulation around the edge.
But this is in conflict with:
The faces can be indistinguishable. They can be transparent.
Marking two faces differently is equivalent to distinguishing between
two opposite senses of circulation around the edge.
The reason is that a bivector is not just a parallelogram made of
segments, but a parallelogram made of directed segments (vectors!)
and in a way (tail to tip!) creating the sense of rotation.
Therefore making the faces transparent would only mask the existing
handedness (chirality), but not eliminate it.
Transparent sides will not eliminate the difference between A^B and B^A!