What about something like the faces of a polyhedron to the vertices of its dual? Additionally, would you count those as highly different, perhaps because a face and a corner feel and look very different when observed physically? Or would they count as similar, perhaps because they’re both geometric ideas used to describe parts of polyhedra and are concepts that are frequently used together rather than being totally unrelated?
That’s really good! I think they count as quite different.
The one thing I don’t like about it is that the dual of the entire geometric object is another, similar geometric object, so on level it only shuffles around vertices and faces. But the vertices themselves become radically transformed, which is great. It’s definitely a better solution than polar/Cartesian coordinates.
What about something like the faces of a polyhedron to the vertices of its dual? Additionally, would you count those as highly different, perhaps because a face and a corner feel and look very different when observed physically? Or would they count as similar, perhaps because they’re both geometric ideas used to describe parts of polyhedra and are concepts that are frequently used together rather than being totally unrelated?
That’s really good! I think they count as quite different.
The one thing I don’t like about it is that the dual of the entire geometric object is another, similar geometric object, so on level it only shuffles around vertices and faces. But the vertices themselves become radically transformed, which is great. It’s definitely a better solution than polar/Cartesian coordinates.