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by iwnit on October 28th, 2009
1) Assuming a convex polyhedron, Euler's formula would applies:
V-E+F = 2
where
V= 20 [number of vertexes]
E= unknown [number of edges]
F=12 [number of faces]
After substitution:
20-E+12=2
E= 30
There would be 30 edges.
An example would be a regular dodecahedron.
Further information:
http://en.wikipedia.org/wiki/Dodecahedron
http://home.att.net/~numericana/data/polyhedra.htm
2) "The Euler characteristic χ was classically defined for the surfaces of polyhedra, according to the formula
χ = V-E+F
where V, E, and F are respectively the numbers of vertices (corners), edges and faces in the given polyhedron. Any convex polyhedron's surface has Euler characteristic
χ = V-E+F = 2
This result is known as Euler's formula."
"The surfaces of nonconvex polyhedra can have various Euler characteristics"
Source and further information:
http://en.wikipedia.org/wiki/Euler's_polyhedron_formula
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You're reading It is given that a polyhedron has 12 faces and 20 vertices. How many edges are there?
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