Can you think of any other solid shapes that have faces that look the same? Do the same number of faces meet at each common vertex?
Other solid shapes with identical faces include:
(1) Cube: 6 square faces, 3 faces meet at each vertex.
(2) Tetrahedron: 4 triangular faces, 3 faces meet at each vertex.
(3) Octahedron: 8 triangular faces, 4 faces meet at each vertex.
∴ Yes, the same number of faces meet at each vertex in these regular polyhedra.
Explanation
The chapter introduces the concept of regular polyhedra (Platonic solids). Besides icosahedron and dodecahedron, there are the cube, tetrahedron, and octahedron. All five have identical regular faces and the same number of faces meeting at each vertex throughout the solid.
Solution Steps
Identify solid shapes with identical faces (regular polyhedra).
Cube: 6 square faces, 3 faces meet at each vertex.
Tetrahedron: 4 triangular faces, 3 faces meet at each vertex.
Octahedron: 8 triangular faces, 4 faces meet at each vertex.
Confirm that the same number of faces meet at each vertex throughout each solid.