Question

a. For each of the Five Platonic Solids, count the number V of vertices, the number F of faces, and the number E of edges. Check that in each case V - E + F = 2

Answer 1

1. The tetrahedron has 4 vertices, 6 edges and 4 faces. Then V-E+F=4-6+4=2

2. The cube has 8 vertices, 12 edges and 6 faces. Then V-E+F=8-12+6=2

3. The octahedron has 6 vertices, 12 edges and 8 faces. Then V-E+F=6-12+8=2

4. The icosahedron has 12 vertices, 30 edges and 20 faces. Then V-E+F=12-30+20=2

5. The dodecahedron has 20 vertices, 30 edges and 12 faces. Then V-E+F=20-30+12=2.