Using Euler’s formula find the unknown

Faces | ? | 5 | 20 |

Vertices | 6 | ? | 12 |

Edges | 12 | 9 | ? |

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 |

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