Gluing Diagrams, part 2

Comments:

The surfaces that can be made by topologically deforming a flat square template and gluing its sides in various arrangements are called flat surfaces. Since some of these surfaces are difficult to visualize, it is easier to work with their gluing diagrams. All of these gluing diagrams have local intrinsic (insider's point of view) geometries equivalent to Euclidean geometry. Local geometry is the geometry observed within a small region of the surface.

Activity 2:

Using the worksheet on page 64, draw a subdivision (tiling) on the gluing diagrams to demonstrate the Euler characteristic of each of the surfaces. Indicate the number of vertices, arcs, and regions for your tilings. Use different colored pens to mark the complete arcs between two points.

Extensions:

What surface does the following gluing diagram represent?