I had the same reaction. Perhaps “vertex” vs “edge” should be used in place of the ambiguous “corner” (which is a vertex in 3D geometry). The 2D projection of

I had the same reaction. Perhaps “vertex” vs “edge” should be used in place of the ambiguous “corner” (which is a vertex in 3D geometry). The 2D projection of the top or side face of object the article shows repeated can be tiled in exactly the same way. It has two vertexes, but those become edges in 3D. In that example the top and one side have 2D projections which are identical except one is rotated 180º from the other. The third face, when projected on a 2D plane, however, is a square. So these shapes have no vertexes (like a cylinder), but they all have edges (like a cylinder). I also think the 3D equivalent - what is the minimum number of edges required for a 3D tessellation - would be interesting.