Using Eulers formula find the unknown
Faces
?
5
20
Vertices
6
?
12
Edges
12
9
?

Faces 6, Vertices 6, Edges 30

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Faces 8, Vertices 8, Edges 30

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Faces 8, Vertices 6, Edges 30

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Faces 8, Vertices 6, Edges 31

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Solution

The correct option is C Faces 8, Vertices 6, Edges 30
Euler's formula is:
Vertices (V) - Edges (E) + faces (F) = 2
For (i) : 12 - 6 + F = 2
Hence, Faces = 8
For (ii) : V - 9 + 5 = 2
Hence, Vertices = 6
For (iii) : 12 - E + 20 = 2
Hence, Edges = 30

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