In each of the following whether they can form a polyhedron or not.
a. 7 faces, 7 vertices, 12 edges
b. 9 faces, 14 vertices, 20 edges

Given:

a. 7 faces, 7 vertices, 12 edges
b. 9 faces, 14 vertices, 20 edges

To do:

We have to find whether the given measurements can form a polyhedron.

Solution:

We know that,

As per Euler’s polyhedron formula $V - E + F = 2$.

Therefore,

(a) $V = 7, F = 7$ and $E = 10$

LHS $=7 - 10 + 7$

$=14-10$

$=4$

RHS $=2$

LHS $≠$ RHS

It cannot form a polyhedron.

 (b) $V = 14, F = 9$ and $E = 20$

LHS $=14 - 20 + 9$

$=23-20$

$=3$

RHS $=2$

LHS $≠$ RHS

It cannot form a polyhedron.

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Updated on: 10-Oct-2022

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