Page 4 - LN3-Polyhedron
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Euler’s formula shows the relationship between edges, faces and vertices of a
polyhedron.
Every polyhedron will satisfy the criterion F + V – E = 2,
Where F is the number of faces of the polyhedron, V is the vertices of the polyhedron and E
is the number of edges of the polyhedron.
Example: Can a polyhedron have 10 faces, 20 edges and 15 vertices?
Sol: Here, F = 10, E = 20 and V = 15
We have:
F + V – E = 2
10 + 15 – 20
or 25 – 20 =5
or 5 2 which is not true
i.e. F + V – E 2
Thus, such a polyhedron is not possible.
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