Question

If a solid shape has $12$ faces and $20$ vertices, then the number of edges in this solid is _____.

Answer 1

Euler's Formula for any polyhedron is $F+V-E=2$.

Where, $F=$ Faces and $V=$ Vertices and $E=$ Edges.

Given: $F=12,V=20$

To Find: Number of edges, $E$

Now, by using the above formula,

$12+20-E=2$

$\Rightarrow 32-E=2$

$\Rightarrow E=30$

So, if a solid shape has $12$ faces and $20$ vertices, then the number of edges in this solid is $30$.