Which of the following cannot be

Solution:

(d) We know that, Euler’s formula for any polyhedron isF+V-E = 2

where, F = faces, V = vertices

and E =edges

(a) $V=4, F=4$ and $E=6$

$\mathrm{LHS}=F+V-E$

$=4+4-6$

$=8-6=2$

 

$=\mathrm{RHS}$

$\therefore$ Option (a) is true for a polyhedron.

(b) $V=6, F=8$ and $E=12$

$\mathrm{LHS}=F+V-E$

$=8+6-12$

$=14-12=2$

 

$=\mathrm{RHS}$

$\therefore$ Option (b) is true for a polyhedron.

(c) $V=20, F=12$ and $E=30$

$\mathrm{LHS}=F+V-E$

$=12+20-30$

$=32-30=2$

 

$=\mathrm{RHS}$

$\therefore$ Option (c) is true for a polyhedron.

(d) $V=4, F=6$ and $E=6$

$\mathrm{LHS}=F+V-E$

$=6+4-6$

 

$=10-6=4 \neq R H S$

$\therefore$ Option (d) is not true for a polyhedron.