Day 28: Heart of Mathematics

• Last time: The Platonic Solids Turn Amorous!

• Today: More about platonic solids
  • Reminders:
    1. you have an assignment due on Friday: the problem solutions from the last section (section 4.3) will be handed in.

  • Construction of a dodecahedron.

  • Why the symmetry in the table we put together for the five Platonic Solids (What is this thing called duality?)?

    	# of Vertices	Edges	Faces	faces at each vertex	sides at each face
    Tetrahedron	4	6	4	3	3
    Tetrahedron	4	6	4	3	3
    Cube	8	12	6	3	4
    Octahedron	6	12	8	4	3
    Dodecahedron	20	30	12	3	5
    Icosahedron	12	30	20	5	3

  • If there's time, we'll look at the other problems:
    • I.2
    • I.3
    • II.1
    • II.2

  • Why only 5 platonic solids?

• Next time: The Fourth Dimension!

Links:

• Java applets allow one to play with Platonic Solids
• Here's a site which shows duality
• And this is the regular polyhedra (spin by mouse!)
• Or use virtual reality software to view them! (your browser will need a special viewer....)