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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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