6. A. An icosahedron has 20 faces. Each face is a triangle.
Show how to use this information to find the number of edges an icosahedron
has.
B. At each vertex of an icosahedron, 5 triangles meet. Use this and the information
in A to find the number of vertices an icosahedron has.
7. Explain how you got the number of vertices. In particular, explain what number you are dividing by and why.
8. A. An octahedron has 8 faces. Each face is a triangle.
Show how to use this information to find the number of edges an icosahedron
has.
B. At each vertex of an octahedron, 4 triangles meet. Use this and the information
in A to find the number of vertices an octahedron has.
9. A. A tetrahedron has 4 faces. Each face is a triangle.
Show how to use this information to find the number of edges a tetrahedron has.
B. At each vertex of a tetrahedron, 3 triangles meet. Use this and the information
in A to find the number of vertices an icosahedron has.
10. A. A cube has 6 faces. Each face is a square. Show how
to use this information to find the number of edges a cube has.
B. At each vertex of a cube, 3 squares meet. Use this and the information in
A to find the number of vertices a cube has.
11. Tell what the dual of the cube is, and explain how you would create the dual if you had a cube.
12. Tell what the dual of the tetrahedron is, and explain how you would create the dual if you had a tetrahedron.
13. Tell what the dual of the icosahedron is, and explain how you would create the dual if you had an icosahedron.
14. Tell what the dual of the dodecahedron is, and explain how you would create the dual if you had a dodecahedron.