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2.1k views
in Mathematics by (15.0k points)

Using Euler’s formula, find the unknown.

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

1 Answer

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Best answer

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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