Question

Can a polyhedron have 5 faces, 7 vertices and 9 edges? give reason​

Answer 1

Answer:

We know from Euler’s formula for polyhedra that F+V=E+2, so there must be (9–5)+2 = 6 vertices. That should give you an idea of what kind of shape this could be. Take two triangles (three edges each) and then join the vertices of the triangles with three more edges. That’s a nine-edged, five faced object (would probably be easiest to envision a prism shape, but it doesn’t have to be.)

Step-by-step explanation:

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Answer 2

SOLUTION

TO DETERMINE

Can a polyhedron have 5 faces, 7 vertices and 9 edges? Give reason

CONCEPT TO BE IMPLEMENTED

Euler’s formula for Polyhedron :

For polyhedron F + V = E + 2

Where F stands for number of faces , V stands for number of vertices , E stands for number of edges .

EVALUATION

By the given ,

F = Number of faces = 5

V = Number of vertices = 7

E = Number of edges = 9

By Euler’s formula F + V = E + 2

LHS = F + V = 5 + 7 = 12

RHS = E + 2 = 9 + 2 = 11

Thus LHS ≠ RHS

Hence Euler’s formula is not Verified

Hence a polyhedron can not have have 5 faces, 7 vertices and 9 edges

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