Identify the number of vertices, edges, and faces of the polyhedron. Use your results to verify Euler's formula.

The Euler's formula relates the number of vertices, faces and the edges of a polyhedron. The given polyhedron has 6 vertices, 10 edges and 6 faces

The Euler's proof is:

First, we count the number of faces of the polyhedron.

This is the flat parts of the shape.

The attached shape has 6 flat surfaces.

So:

Next, we count the number of edges.

This is where two faces meet.

The attached shape has 10 edges;

So:

Lastly, we count the number of vertices.

This is where two edges meet.

The attached shape has 6 vertices.

So:

Using Euler's formula, we have:

Substitute values for V, E and F

Hence, the polyhedron has 6 vertices, 10 edges and 6 faces

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