Math 444, Monday, November 3

Class: Building and Analyzing Cubes

Part 1: Polydron cube

• Make a cube with Polydrons. Look at cutting by planes.
• From an index card, cut out a rectangle that is approximately a diagonal cross-section of the cube.
• Tell the (theoretical) dimensions of this rectangle if the cube has edge length s.
• Then tell the radius of the insphere and circumsphere of the cube.

Part 2: Nets

• Find nets for a cube using polydrons. (This is a connected figure made up of 6 squares that can be cut out, folded and taped to make a cube.)
• Discuss a net for a square-based pyramid with vertex on a vertex of the cube.

Part 3. Square Based Pyramid with Equilateral Triangle faces.

Discussion of dihedral angle computed from cross-section.