Lesson Six — Dual Pairs

From: www.PlatonicSolids.info

 

 

Prep

• Cut out paper squares, triangles, and pentagons.
• Cut out the three types of stellate patterns
• Create the five Platonic Solids.
• Use the stellate patterns to glue a little pyramid on each face.
• You now have two versions of two of the stellated polyhedra and one version of the third.
• Load the video into a dvd player and make sure you can select the “Dual Pairs” chapter.  In order to do this, you must click on the arrow on the lower right of the first menu to get to the second menu.
• Practice playing the scene and pausing it once all of the text appears.
• Prepare enough paper patterns for all of the students to create their own dual pairs.

 

Procedure

• Play the “Duals Pairs” scene from the video.
• Pause the video once all of the text has appeared.
• Ask the students if they see a pattern in the number of faces meeting at each vertex and the number of sides on each face of the members of the dual pairs.
• Also ask students if they see if a pattern in the total number of vertices, the total number of faces, and the total number of edges of the members of the dual pairs.
• Revisit Euler’s formula and see what happens to the result if the values for V and F are swapped.
• Show the students your stellated polyhedra.
• Pass out the materials and help students make their own stellated polyhedra.