Given:
The given shape is a polyhedron.
Required:
We need to use Euler's formula for the given shape.
Explanation:
Consider Euler's formula.
[tex]V-E+F=2[/tex]
where V is the number of vertices, E is the number of edges and F is the number of faces.
Recall that a vertex is a corner.
The number of corners in the given shape is 12.
[tex]V=12[/tex]
Recall that an edge is a line segment between faces and a face is a single flat surface.
The number of edges in the given shape is 18.
[tex]E=18[/tex]
The number of faces in the given shape is 8.
[tex]F=8[/tex][tex]V-E+F=12-18+8[/tex][tex]V-E+F=2[/tex]
The given shape satisfied Euler's formula.
So it is a polyhedron.
Final answer:
[tex]V=12[/tex]
[tex]E=18[/tex]
[tex]F=8[/tex]
[tex]V-E+F=2[/tex]
The given shape is a polyhedron.
