Chapter 9.4, Problem 6E

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6th Edition

Daniel C. Alexander + 1 other

ISBN: 9781285195698

Textbook Problem

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A regular polyhedron has 12 edges and 8 vertices.

a) Use Euler’s equation to find the number of faces.

b) Use the result from part (a) to name the regular polyhedron.

To determine

(a)

**To find:**

The number of faces using 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.

6) A regular polyhedron is a convex polyhedron whose faces are congruent regular polygons.

7) A regular hexahedron is a regular polyhedron with six congruent square faces.

B) Eulerâ€™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

To determine

(b)

**To find:**

The name of regular polyhedron.

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