Can a polyhedron have 12 faces , 22 edges and 17 vertices? Verify using the Euler’s formula.
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Answer:
No polyhedron has 12 faces, 22 edges, and 17 vertices.
No polyhedron has 12 faces, 22 edges, and 17 vertices.
Step-by-step explanation:
Consider the provided information.
It is given that we need to make a polyhedron having 12 faces, 22 edges and 17 vertices.
According to Euler's polyhedron formula:
V - E + F = 2
Where V is the number of vertices, E is the number of edges and F is the number of faces.
Now, simply substitute the number of faces, edges, and vertices in the above formula.
17-22+12=217−22+12=2
29-22=229−22=2
7=27=2
Which is not true.
Thus, No polyhedron has 12 faces, 22 edges, and 17 vertices.
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