Question

Using Euler’s formula, find the unknown:

Faces	?	5	20
Vertices	6	?	12
Edges	12	9	?

Answer 1

In first column, F = ?, V = 6 and E = 12
Using Euler’s formula, we see F + V – E = 2
F + V – E = 2
=> F + 6 – 12 = 2
=> F – 6 = 2
=> F = 2 + 6 = 8
Hence there are 8 faces.
In second column, F = 5, V = ? and E = 9
Using Euler’s formula, we see F + V – E = 2
F + V – E = 2
=> 5 + V – 9 = 2
=> V – 4 = 2
=> V = 2 + 4 = 6
Hence there are 6 vertices.
In third column, F = 20, V = 12 and E = ?
Using Euler’s formula, we see F + V – E = 2
F + V – E = 2
=> 20 + 12 – E = 2
=> 32 – E = 2
=> E = 32 – 2 = 30
Hence there are 30 edges.