Euler's Polyhedral Formula: Difference between revisions
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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>. | ||
==Observe!== | |||
Apply Euler's Polyhedral Formula on the following polyhedra: | |||
<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]] | ||
{{stub}} | {{stub}} | ||
Revision as of 07:59, 23 June 2009
Let 
be any convex polyhedron, and let 
, 
and 
denote the number of vertices, edges, and faces, respectively. Then 
.
Observe!
Apply Euler's Polyhedral Formula on the following polyhedra:
See Also
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