#### Question

Using Euler’s formula, find the unknown.

Faces |
? | 5 | 20 |

Vertices |
6 | ? | 12 |

Edges |
12 | 9 | ? |

#### Solution

By Euler’s formula, we have

F + V − E = 2

(i) F + 6 − 12 = 2

F − 6 = 2

F = 8

(ii) 5 + V − 9 = 2

V − 4 = 2

V = 6

(iii) 20 + 12 − E = 2

32 − E = 2

E = 30

Thus, the table can be completed as

Faces |
8 | 5 | 20 |

Vertices |
6 | 6 | 12 |

Edges |
12 | 9 | 30 |

Is there an error in this question or solution?

Solution Using Euler’S Formula, Find the Unknown. Concept: Faces, Edges and Vertices.