Thursday,  October 2

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Space: How do we understand objects in space? Continued..
More on  understanding the torus...

Cross sections: circles.... cell mitosis

Shadows:

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!
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  The 5 Platonic Solids

  Cube Dodecahedron Icosahedron Octahedron Tetrahedron

• Regular polygons around a vertex.
• All vertices are "the same"
• We worked on the activity in counting vertices, edges, and faces for the platonic solids to become more familiar with them.
• The Archimedean  Solids:

• The 13 Archimedean Solids

  Cubeoctahedron Icosidodecahedron Rhombicubeoctahedron Rhombicosidodecahedron Rhombitruncated Cubeoctahedron Rhombitruncated Icosidodecahedron Snub Cube Snub Dodecahedron Truncated Cube Truncated Dodecahedron Truncated Icosahedron Truncated Octahedron Truncated Tetrahedron



• Symmetries (Isometries) in the plane compared to those in space- an introduction: Symmetries of the Platonic Solids: Consider the Tetrahedron and the Octohedron
  
• Rotations: Center point(in the plane) - central axis ( in space)
  
• Reflection :  across line (in the plane) - across plane (in space)
  
• Symmetries of the cube:
• Rotations
• reflections
• rotation- reflection

• More on The regular and semiregular polyhedra: Check this site!  from Visual geometry pages.
  
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• Isometries in space: products of reflections in space:
• Rotations and translations
• Applications to dance