Thursday,  February 26

Space: How do we understand objects in space? Continued..

• analogue...  point... line.... polygon.... polyhedron......
• Some Issues we'll consider in space:
• Polyhedra and symmetry.
• Historical Note on Kepler.

More on  understanding the torus...

Cross sections: circles.... cell mitosis

Fold downs- flattened figures:

• Polyhedra and symmetry.
• What's at the Junkyard? Models of platonic solids! look at deltahedra!
• Platonic (regular convex polyhedra) and Archimedean (semiregular convex) Solids- on the web!
• The 5 Platonic Solids

Octahedron   Tetrahedron   Icosahedron
Cube                                  Dodecahedron
• Why are there only 5?
• Look at the possible ways to put a single regular polygon together with more of the same to make a spatial "cap" about a single vertex. This involves equilateral triangles (3,4, or 5), squares (3) or pentagons (3).
• This shows that there were at most five vertex caps possible. These actually do work to make
• Regular polygons around a vertex.
• All vertices are "the same"
• Activity: Counting vertices, edges, and faces for the platonic solids to become more familiar with them.
•  The 13 Archimedean Solids