A polyhedron has 32 edges and the number of faces is 5 less than twice the number of vertices. How many faces of this polyhedron has?
Answers
Given : A polyhedron has 32 edges and the number of faces is 5 less than twice the number of vertices.
To Find : How many faces of this polyhedron has?
Solution:
Number of Faces = F
Number of faces is 5 less than twice the number of vertices.
=> F = 2V - 5
=> F + 5 = 2V
=> V = (F + 5)/2
Edges E = 32
Euler formula for faces = Edges - Vertex + 2
=> F = E - V + 2
=> F = 32 - (F + 5)/2 + 2
=> F = 34 - (F + 5)/2
=> 2F = 68 - F - 5
=> 3F = 63
=> F = 21
Faces of this polyhedron are 21
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