# Using Euler’s formula, find the unknown.

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Using Euler’s formula, find the unknown.

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

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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