1. Let S be the surface with the following polygonal decomposition: d g b d a) How many vertices does S have? Justify your answer. b) How many boundary circuits does S have? c) Give a polygonal decomposition for S that has only one polygon. d) Is S orientable? e) Compute the Euler characteristic for S. f) Give the standard form for S. g) Describe S as a standard surface: a sphere with punctures, handles and crosscaps. 2. For each of the following properties, give an example of a connected surface with that property or explain why such a surface does not exist. If the surface does exist then draw its standard polygonal decomposition. a) An oriented surface with Euler characteristic 3. b) A non-oriented closed surface with Euler characteristic -4. 3. Give a complete list of all the (connected) oriented surfaces with Euler characteristic -5, written in standard form.