Question

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

Answer 1

Solve for the number of edges:

Given that the solid shape has $12$ faces and $20$ vertices.

Euler’s formula for any polyhedron is $F+V–E=2$ where $F,V,E$ are number of faces, vertices and edges respectively.

Here $F=12,V=20$ and substituting in the above formula we get

$\begin{array}{crcl}& 12+20-E& =& 2\\ \Rightarrow & E& =& 12+20-2\\ \Rightarrow & E& =& 30\end{array}$

Hence, the number of edges in this solid are $30$.