Chapter 9.4, Problem 3E

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6th Edition

Daniel C. Alexander + 1 other

ISBN: 9781285195698

Textbook Problem

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For figure (b) of Exercise 1, find the number of faces, vertices, and edges in the polyhedron. Then verify Euler’s equation for that polyhedron.

To determine

**To find:**

The number of faces, vertices and edges in the polyhedron and verify Euler’s equation.

Explanation

**Approach:**

A) Polyhedron

1) A polygon is a two dimensional shape form with more than two straight lines.

2) A polyhedron is a three-dimensional solid shape.

3) Each flat surface of a polyhedron is a polygon and is called a face.

4) The line segment where two faces of a polyhedron meet is called an edge.

5) The point where three or more edges of a polyhedron meet is called a vertex.

B) Euler’s Equation

A very important relationship between the number of vertices, faces and edges of solid shapes was discovered by a Swiss mathematician Leonard Euler.

It states

Where, *V*=Number of vertices*, F*=number of faces, *E*=number of edges.

**Calculation:**

In the polyhedron EFGHIJK,

The number of vertices (*V*) =7(E, F, G, H, I, J, K)

Number of faces (*F*) =9(

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