Answer :

Given: The following

[tex]\begin{gathered} N_{umber\text{ of faces}}=7 \\ N_{umber\text{ of vertices}}=10 \end{gathered}[/tex]

To Determine: The number of edges

Solution:

The Euler's formula is given as

F + V = E + 2,

where F is the number of faces,

V the number of vertices, and

E the number of edges.

Substitute the given into the formula

[tex]\begin{gathered} F=7 \\ V=10 \\ E=? \end{gathered}[/tex][tex]\begin{gathered} F+V=E+2 \\ E=F+V-2 \\ E=7+10-2 \\ E=17-2 \\ E=15 \end{gathered}[/tex]

Hence, the number of edges possessed by the polyhedron is 15

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