8 types of shape

A random thought from the other day is that shapes can be categorised by the presence or not of faces, edges and corners. That's a 3D table so I'll fill it in as two 2x2 tables:

faces:

	Edges	No edges
Corners
No corners

no faces:

	Edges	No edges
Corners
No corners		.

For the object with no faces but edges and corners, you can see the corners as protrusions on the top side, and the edges when viewed on the bottom side.

The spikey object (bottom left) with only appears to have corners because I have cropped it to finite size, but the basic structure is unbounded and all those corners connect to another to make continued curved edges.

The object with no faces, corners or edges is probably just a point, or just nothing.