Lesson Eight — Research Reports

From: www.PlatonicSolids.info

Prep

- Create a list of possible research project questions.
- Here are some possible ideas:

- What other groups of polyhedra exist?
- What do you get when you connect the midpoints of the edges of the Platonic solids?
- What do you get when you connect the points of the stellated polyhedra?
- What are the shapes of the different cross-sections of the Platonic solids.
- What are the shapes of the different shadows of the Platonic solids?
- How can you calculate the surface areas of the Platonic solids?
- How can you calculate the volumes of the Platonic solids?
- How do the surface areas of the Platonic solids compare to the surface area of a sphere?
- How did Kepler use the Platonic solids?
- What significance did Plato give to his solids?
- Which polyhdra can be close packed?
- What possible truss structures can be made from tetrahedra and octahedra?
- How are geodesic domes related to polyhedra?
- What kinds of polyhedra are naturally formed as crystals?
- What polyhedra are found in molecular structures?
- What is Buckminsterfullerine (Bucky Balls)?
- What polyhedra can be found in the art of M. C. Escher?
- What is the golden mean and how is it related to the Platonic solids?

Procedure

- Assign students to do a research project.
- They can use the links on the www.PlatonicSolids.info site.
- They can search the web themselves (If they use the search engine on the site above, it will restrict them to appropriate geometry sites.).
- They can build models and conduct their own experiments.