Thursday, October 13
Review and finish counting activity of polyhedra.
Problem 1:
Do some systematic counting
Notice pairings
Discuss connection of face  vertex.
Nesting of
cube inside octa inside cube ...
icoso inside dodeca inside icoso....
tetra inside tetra inside tetra ...
Problem 2:
More pairings
Notice double counting products = 2*number of edges.
[maybe V + F = E + 2?]
Symmetries (Isometries)
in the plane
compared to those
in space

A continuation of the use of analogy.
Rotations: Center point  central axis
Reflection : across line  across plane
Symmetries of the octahedron ( Do for the class) 
4 fold
rotational axes
determined by opposite vertices. 3
2 fold
rotational axes
determined by midpoints of opposite sides. 6
3 fold
rotational axes
determined by midpoints of opposite equilateral triangle faces: 4
Reflections
across planes mid way between
opposite vertices
: 3 (equators)
Reflections
across planes midway between
opposite sides
: 6
symmetries of the cube (Activity):
Rotations
reflections