Solutions
1. A dodecahedron has 12 faces. Each face is a pentagon (5 sides). Show how to use this information to find the number of edges a dodecahedron has.
12x5/2=60/2=30 edges
2. Explain the formula or process you used to find the number of edges a dodecahedron has. Include an explanation of why you divide by 2 as part of the formula
You multiply 12x5 to find the number of edges on 12 pentagons.
Then, you divide by 2 because when you put the pentagons together, two edges go next to each other to make one edge.
3. Sample problem. A dodecahedron has 12 faces. Each face is a pentagon (5 vertices), and at each vertex there are 3 faces that meet there. Show how to use this information to find the number of vertices a dodecahedron has
12x5/3=60/3=20 vertices
4. Sample problem. Tell what the dual of the Octahedron is, and explain how you would create the dual if you had an octahedron.
The dual of the octahedron is the cube. You could create this by putting a dot in the center of each of the faces of the octohedron. This would be 8 vertices for the new polyhedron. Then you would connect those dots with edges (an edge would connect the two dots on adjacent faces), and faces.
Also
| Shape of each face | number of faces meeting at each vertex | name of polyhedron |
| Eq triangle | 3 | Tetrahedron |
| Eq triangle | 4 | Octahedron |
| Eq triangle | 5 | Icosahedron |
| Square | 3 | Cube |
| Reg. Pentagon | 3 | Dodecahedron |