Reconceptualizing Mathematics book Section 172 Learning Exer

Reconceptualizing Mathematics book. Section 17.2. Learning Exercises #1

Solution

Reconceptualizing Mathematics book. Section 17.2. Learning Exercises #1

(a) faces = 8, vertices = 12, and edges = 18

(b) faces = 5, vertices = 6, and edges = 9

(c) faces = 6, vertices = 8, and edges = 12

The geometrical formula V E + F = 2, where V, E, and F are the numbers of vertices, edges, and faces of any simple convex polyhedron or of an equivalent topological graph.

By using above relation let us verify the plyhedra given in Parts (a), (b) and (c) as below:

(a) Faces F = 8, Vertices V = 12, and Edges E = 18

  V E + F = 12 - 18 + 8 = 2 Which verifies Euler\'s formula

(b)  Faces F = 5, Vertices V = 6, and Edges E = 9

  V E + F = 6 - 9 + 5 = 2 Which verifies Euler\'s formula

(c)  Faces F = 6, Vertices V = 8, and Edges E = 12

  V E + F = 8 - 12 + 6 = 2 Which verifies Euler\'s formula