I was doing a spot of light reading (crystallography), when the term "convex" polyhedron came up in a a section (very prominently) in conjunction with something else called the "Euler characteristic".
The Wikipedia article (linked above) on the "Euler characteristic" is written in the same vein as the book I'm using... but try as I might, I can't seem to understand it :/
Excerpt from the section (in the Wiki article) in question.
I suppose my inability to fully comprehend the section (relevant excerpt included above) is due to my shortcomings as a high-school student; so following the other Wiki links wasn't much help...and neither was Google.
Can someone explain (in a way a high-school student such as myself would understand),
1) What is a "convex" polyhedron?
2) What's this "Euler characteristic" all about? Does it have any sort of physical implications (by "physical", I mean "geometry" of the solid)?
(Including my thoughts on this...in case it helps a potential answerer in tailoring an answer best suited to my needs/understanding)
Looking at the figures/models/diagrams provided in the Wiki article, has led me to believe that "convex" polyhedra must be the same as (or at least, very similar to) the idea of a "regular" polyhedra (identical faces, sides and dihedral angles) that we've learned when we were younger...except the corresponding Wiki article on "convex" polyhedra does not reflect this simplicity; so drawing such an equivalence appears to be wrong.
I have not studied "Topology" (at least, not as a field of mathematics). Obviously, I'm quite capable of looking at 3D object and classifying it as a "cube", a "sphere", some sort of "prism", etc...but my knowledge of "topology" pretty much ends there. I'm sorry.
I was tempted to ask the question ("What's a convex polyhedron?", "What's the Euler characteristic?") separately. However, seeing as they're intimately linked (at least, from the crystallography perspective), I felt it more prudent to put these questions in a single post.