Question

Verify Euler's formula for these solids.

Answer 1

The given figure has 8 faces, 18 edges and 12 vertices, i.e., E = 18, F = 8 and V = 12.
According to Euler's formula,
V $-$ E + F = 2
Here,
L.H.S. = V $-$ E + F
= 12 $-$ 18 + 8
= 2
And,
R.H.S. = 2
Thus, we have:
L.H.S. = R.H.S.
Hence, Euler’s formula is verified.