Some thoughts on the dimensions of polyhedra and polygons: How to make a 3D polygon with no area

A polyhedron is just a bunch of faces connected by edges. All the vertices are closed, so there’re no open bits. So there’s no rule that a polyhedron has to be 3D. A grid can also be a polyhedron! In fact, it’s also a regular polyhedron as all its vertices, edges and faces are the same and all its faces are regular.

In the same way, polygon doesn’t have to be 2D!

You can also make a 1D polygon. With infinitely many sides.
A zigzag is also a regular polygon because you can invert it. All the edges are the same size and all the angles are the same size. It’s an infinite regular polygon!

You can also curl this zigzag into the 3rd dimension, turn it into a loop et voilà – now you’ve got a 3D polygon! This polygon doesn’t have an area anymore, because it doesn’t have an exterior or an interior.

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