## Edges and Faces: A Matter of Definition

(An archive question of the week) Having looked at the matter of faces, edges, and vertices from several different perspectives, I want to look at one more question and answer, to tie it all together.

(An archive question of the week) Having looked at the matter of faces, edges, and vertices from several different perspectives, I want to look at one more question and answer, to tie it all together.

Having discussed how to count faces, edges, and vertices of polyhedra, and then looked at Euler’s formula that relates them (not only in polyhedra but in graphs on planes and other surfaces), we need to consider a question we have received at least 100 times: Are these terms even defined (or defined correctly) for cylinders, …

Do Curved Surfaces Have Faces, Edges, and Vertices? Read More »

(A new problem of the week) Having discussed counting earlier this week, let’s take a look at a different kind of counting. The subject of combinatorics (the study of counting) arises in many guises: probability, sets, geometry. Here, we look at a relatively basic type of problem that involves the same sort of organized thinking …