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Consider following figure with n = 4.
Clearly, number of vertices (v) = 14, number of edges (e) = 24 and number of faces (f) = 12.
According to Euler's formula, v + f = e + 2
i.e. v + f = 14 + 12 = 26 = e + 2.
In general we have, v = 2n + nC2 and e = 2n + n2.
Hence, using Euler's formula,
f = e + 2 - v
= 2n + n2 + 2 - 2n + nC2
After simiplication we have,
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