A polyhedron has number of vertices equal to $32$ times of number of faces. If a polyhedron has 8 edges, then find the number of vertices and faces.

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number of faces = 4 number of vertices = 6

number of faces = 8 number of vertices = 12

number of faces = 7 number of vertices = 5

number of faces = 9 number of vertices = 12

answer is A.

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Detailed Solution

It is given a polyhedron.
Let the number of faces = F.
So, number of vertices =

3 F 2

.
Number of edges = 8.
By Euler’s formula for polyhedron, F + V = E + 2.

⇒ F + 3 F 2 = 8 + 2

⇒ 5 F 2 = 10

⇒ F = 10 × 25

⇒

F = 4
Hence, number of faces = 4, number of vertices = 6.
Therefore, the correct option is 1.

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