Difference between revisions of "Euler's Polyhedral Formula"

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Let <math>P</math> be any [[convex]] [[polyhedron]], and let <math>V</math>, <math>E</math> and <math>F</math> denote the number of [[vertex|vertices]], [[edge]]s, and [[face]]s, respectively. Then <math>V-E+F=2</math>.
 
Let <math>P</math> be any [[convex]] [[polyhedron]], and let <math>V</math>, <math>E</math> and <math>F</math> denote the number of [[vertex|vertices]], [[edge]]s, and [[face]]s, respectively. Then <math>V-E+F=2</math>.
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==Observe!==
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Apply Euler's Polyhedral Formula on the following polyhedra:
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<math> \begin{tabular}{|c|c|c|c|}\hline Shape & Vertices & Edges & Faces\\ \hline Tetrahedron &4  &6 & 4 \\ \hline Cube/Hexahedron & 8 & 12 & 6\\ \hline Octahedron & 6 & 12 & 8\\ \hline Dodecahedron & 20 & 30 & 12\\ \hline \end{tabular} </math>
  
 
== See Also ==
 
== See Also ==
  
 
* [[Euler characteristic]]
 
* [[Euler characteristic]]
 
  
 
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Revision as of 08:59, 23 June 2009

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:

$\begin{tabular}{|c|c|c|c|}\hline Shape & Vertices & Edges & Faces\\ \hline Tetrahedron &4  &6 & 4 \\ \hline Cube/Hexahedron & 8 & 12 & 6\\ \hline Octahedron & 6 & 12 & 8\\ \hline Dodecahedron & 20 & 30 & 12\\ \hline \end{tabular}$

See Also

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