I have a math test coming up tomorrow. One of the topics will be triangulation. My teacher put up some questions we could try out.I am quite stumped by one of them, however, and would love some help with it.
"Draw a different triangulation of the surface area of the sphere than the one we have drawn below, and describe them both. Let V = “number of vertices”, E = “number of edges” and F = “number of faces”. Calculate V-E+F for both triangulations of the sphere surface areas. Is there anything you notice?" The triangulation in question
I was wondering if you guys could help me calculate Euler's Characteristic for the figure in question, and maybe help me draw another triangulation?
Thanks in advance!
Hint : fix a triangulation $t$. What happened if you subdivide your triangulation with only one more triangle ? Can you always relate two triangulations ?