Using Euler's formula find the unknown: Faces ? 5 20 Vertices 6 ?… - Vidyadip

Question

Using Euler's formula find the unknown:

Faces	$?$	$5$	$20$
Vertices	$6$	$?$	$12$
Edges	$12$	$9$	$?$

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Answer

We know that the Euler's formula is: $F + V = E + 2$
$i.$ The number of vertices $V$ is $6$ and the number of edges $E$ is $12$.
Using Euler's formula:
$F + 6 = 12 + 2$
$F + 6 = 14$
$F = 14 - 6$
$F = 8$
So, the number of faces in this polyhedron is 8.
$ii.$ Faces, $F = 5$
Edges, $E = 9$
We have to find the number of vertices.
Putting these values in Euler's formula:
$5 + V = 9+ 25 + V = 11$
$V = 11 - 5$
$V = 6$
So, the number of vertices in this polyhedron is $6$.
$iii.$ Number of faces $F = 20$
Number of vertices $V = 12$
Using Euler's formula:
$20 + 12 = E + 2$
$32 = E + 2$
$E + 2 = 32$
$E = 32 - 2$
$E = 30$
So, the number of edges in this polyhedron is $30$.

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