AoPSWiki

Our Precalculus course starts on Dec. 4. Master trig, complex numbers, and vectors and matrices in 2 and 3 dimensions. Click here to enroll today!

Personal tools

Search

Toolbox

Euler's Polyhedral Formula

From AoPSWiki

Let $P$ be any convex polyhedron, and let $V$ , $E$ and $F$ denote the number of vertices, edges, and faces, respectively. Then $V-E+F=2$ .

Observe!

Apply Euler's Polyhedral Formula on the following polyhedra:

$\begin{tabular}{|c|c|c|c|}\hline Shape & Vertices & Edges & Faces\\ \hline Tetrahedron &4 &6 & 4 \\ ...$

See Also

Euler characteristic

This article is a stub. Help us out by expanding it.

Retrieved from "http://www.artofproblemsolving.com/Wiki/index.php/Euler%27s_Polyhedral_Formula"

Categories: Stubs | Theorems | Geometry

Want to learn how to tackle those tough AMC/AIME/Olympiad counting and probability problems? Check out Art of Problem Solving's Intermediate Counting & Probability by David Patrick.

© Copyright 2008 AoPS Incorporated. All Rights Reserved. • Foundation • Privacy • Contact Us