Course Summary 3

 

8. Regular another polyhedra.

* There are only 5 regular polyhedra (and we saw why that is true).

* There are many more (92 or so) convex polyhedra with sides made of (possibly distinct) regular polygons.

* A link to the playground.

 

9. Hyperbolic Plane and tilings in the hyperbolic plane .

* Hyperbolic plane: what is it.

* "Lines" in the hyperbolic plane and how to construct them.

* Other constructions: parallel "lines", triangles, angles between "lines".

* (Regular) tilings of the hyperbolic plane - infinitely many such (since the sum of the angles in a hyperbolic triangle could be any angle between 0 and 180 degrees).

 

10. Topology .

* Homotopic objects: two object such that one can be deformed into the other without cutting or gluing.

 

 

 

 

*Various (topological) objects we have encountered (and we saw how to get them).