Reading assignment spherical geometry - Part 2

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Carefully read the sections 6-12 and answer the following questions:

  • Q1. What is the Euler characteristic?
  • Q2. What is the dual of a tessellation? What is the dual of a cube?
  • Q3. What do we know about translations and rotations on the sphere? Are they related?
  • Q4. Follow the link to the Wikipedia page about symmetry groups of the sphere. The page divides the symmetries in different types. What are they?
  • Q5. What is most surprising to you about spherical geometry after reading the spherical geometry section?