Homework 3

This homework is due on Thursday, February 25, right before class.

• Alex: 5.3/4, 5.3/12, 5.3/18, 5.4/22, 5.4/8, 5.4/14, 5.4/35, question 1 below, question 4 below,
• Amilcar: 5.3/4, 5.3/7, 5.3/20, 5.4/22, 5.4/8, 5.4/15, 5.4/35, question 1 below, question 3 below,
• Bobby: 5.3/4, 5.3/7, 5.3/20, 5.4/22, 5.4/7, 5.4/13, 5.4/35, question 2 below, question 4 below,
• Caitlin: 5.3/4, 5.3/12, 5.3/20, 5.4/23, 5.4/9, 5.4/13, 5.4/35, question 2 below, question 3 below,
• Callie: 5.3/3, 5.3/7, 5.3/20, 5.4/23, 5.4/9, 5.4/15, 5.4/35, question 1 below, question 3 below,
• Carlos: 5.3/3, 5.3/7, 5.3/18, 5.4/22, 5.4/8, 5.4/15, 5.4/29, question 1 below, question 3 below,
• Colin: 5.3/2, 5.3/6, 5.3/20, 5.4/22, 5.4/8, 5.4/13, 5.4/30, question 2 below, question 4 below,
• Diego: 5.3/4, 5.3/12, 5.3/20, 5.4/23, 5.4/9, 5.4/16, 5.4/30, question 2 below, question 4 below,
• Frank: 5.3/3, 5.3/7, 5.3/20, 5.4/22, 5.4/7, 5.4/14, 5.4/30, question 2 below, question 3 below,
• Jessica: 5.3/4, 5.3/6, 5.3/19, 5.4/22, 5.4/9, 5.4/15, 5.4/35, question 1 below, question 4 below,
• Jonathan: 5.3/1, 5.3/12, 5.3/18, 5.4/22, 5.4/9, 5.4/15, 5.4/29, question 2 below, question 4 below,
• Jordan: 5.3/3, 5.3/6, 5.3/20, 5.4/23, 5.4/8, 5.4/13, 5.4/30, question 1 below, question 4 below,
• Lacie: 5.3/3, 5.3/12, 5.3/18, 5.4/23, 5.4/9, 5.4/13, 5.4/30, question 2 below, question 3 below,
• Madison: 5.3/2, 5.3/12, 5.3/20, 5.4/23, 5.4/8, 5.4/16, 5.4/29, question 1 below, question 4 below,
• Milani: 5.3/3, 5.3/6, 5.3/19, 5.4/23, 5.4/8, 5.4/13, 5.4/30, question 1 below, question 3 below,
• Mikhail: 5.3/3, 5.3/12, 5.3/20, 5.4/22, 5.4/8, 5.4/15, 5.4/30, question 2 below, question 4 below,
• Mounia: 5.3/1, 5.3/7, 5.3/20, 5.4/23, 5.4/7, 5.4/15, 5.4/29, question 1 below, question 4 below,
• Nada: 5.3/4, 5.3/12, 5.3/19, 5.4/22, 5.4/9, 5.4/13, 5.4/29, question 2 below, question 4 below,
• Rozie: 5.3/2, 5.3/12, 5.3/20, 5.4/23, 5.4/7, 5.4/13, 5.4/30, question 2 below, question 3 below,
• Salem: 5.3/4, 5.3/7, 5.3/18, 5.4/23, 5.4/8, 5.4/13, 5.4/29, question 1 below, question 3 below,
• Sarah: 5.3/2, 5.3/12, 5.3/20, 5.4/23, 5.4/9, 5.4/14, 5.4/29, question 2 below, question 3 below,
• Sonja: 5.3/1, 5.3/12, 5.3/20, 5.4/23, 5.4/8, 5.4/15, 5.4/30, question 2 below, question 3 below,
• Stephen: 5.3/4, 5.3/6, 5.3/20, 5.4/22, 5.4/8, 5.4/15, 5.4/35, question 1 below, question 3 below,
• Verena: 5.3/2, 5.3/12, 5.3/20, 5.4/22, 5.4/9, 5.4/14, 5.4/29, question 1 below, question 3 below,

1. Draw the plane graph of the following polyhedron:

   

2. A connected plane graph has nine vertices having degress 2, 2, 2, 3, 3, 3, 4, 4, and 5. How many edges are there? How many regions?
3. Is there a plane graph without vertices of degree 6 or less? Try to find one, and if you don't succeed, describe why you cannot find some. A proof would even be better.
4. Find the dual of the following graph.