Answer:
Number of vertices are 34.
Step-by-step explanation:
The relation between the number of vertices, number of edges and number of faces was given by Euler's formula, which is as under:
[tex]F + V - E =2[/tex]
Where [tex]F[/tex] is the number of faces in the polyhedron.
[tex]V[/tex] is the number of vertices in the polyhedron and
[tex]E[/tex] is the number of edges in the polyhedron.
Let us try to apply this formula in a cube. We know that number of vertices are 8, number of edges are 12 and number of faces are 6.
6 + 8 - 12 [tex]\Rightarrow 2[/tex]
Hence, the formula is applicable.
Applying Euler's formula in the given question.
F = 14
E = 46
V = ?
Using Euler's Formula:
[tex]14 + V - 46 = 2 \\\Rightarrow V = 2 + 32\\\Rightarrow V = 34[/tex]
Hence, number of vertices are 34.
