- Sorry: I still don't have your last homework graded.
- You have a homework due today.
- Star Polygons (for Nathanial). Be thinking of your logos!
- Today we continue talking about the Platonic solids
- Review and extension of Platonic
solids
- From the October 7th, 2011 New York Times
- What can you do with a dodecahedron?
- Icosahedral
- amoeboid protozoa Circogonia icosahedra
- Viruses:
- The Cliff Notes Version...
"An array of viruses. (a) The helical virus of rabies. (b) The segmented helical virus of influenza. (c) A bacteriophage with an icosahedral head and helical tail. (d) An enveloped icosahedral herpes simplex virus. (e) The unenveloped polio virus. (f) The icosahedral human immunodeficiency virus with spikes on its envelope."
- Bacteriophages and Virions
- The Cliff Notes Version...
- Dodecahedral
- Viruses:
- Viruses:
- amoeboid protozoa Circogonia icosahedra
- There are exactly five platonic solids:
Tetrahedron Hexahedron
or CubeOctahedron Dodecahedron Icosahedron 
- Last time we created a set of Platonic solids in 3-d, using
a paper template.
One of the advantages of making a nice set of these is that you will be able to use them, with anything you want written on them, for the next exam. They
- must be constructed -- built! no flat versions -- from an 8.5x11 piece of paper (just like the one I give you in class); and
- You can't undo them during the test.
- Now: once you have a nice set, you can fill in the following table:
# of Vertices # of Edges # of Faces # of Faces at each Vertex # of Edges at each Face Tetrahedron Cube Octahedron Dodecahedron Icosahedron What conclusions can we draw from this data? Is there a pattern?
- From the October 7th, 2011 New York Times
- Duality
- Each Platonic solid has a "twin" -- called its dual -- which we can discover from the table.
- Duality in nature:
- Each Platonic solid has a "twin" -- called its dual -- which we can discover from the table.
- How can we draw the Platonic solids on a sheet of paper? We project them onto a piece of paper.
- The cube you've undoubtedly done before.
- The tetrahedron can be drawn to be a "distorted" Mercedes symbol
- Here are all the solids. Practice drawing them! Where's the duality?
- Review and extension of Platonic
solids
- Java applets allow one to play with Platonic solids
- A Treatise on Symmetry
- hexagonal graph paper (make your own!)
- Platonic solids in 2-D (paper template)
- concave versus convex (an animation)