On the wikipedia article explaining exterior algebra, this figure is shown, visualizing the relationship between the wedge product of 2 vectors (or differential forms for that matter), and the "orientation" of the resulting 2-Form or 3-Form on $\mathbb{R}^3$.
In the 3-Form case, the orientation of the facets are shown with the circles. 1 Observation is, that faces with the same orientation as the vectors indicate, face the camera, where the others are in the opposite orientation. Why is that?
Also, why would these faces be oriented in this particular way? In what way is the 3-forms orientation related to the 2-forms making up it's faces?