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Now we could query our selves a couple of concerns

Performs this process of removing faces actually prevent, and, whether or not it does, exactly what are i kept having? A tiny idea can tell you so it need to end - there are just finitely many face and corners we are able to treat - hence in the event it does, we are kept having just one triangle. You can view some diagrams outlining the complete process for the network shaped off a beneficial dodecahedron (keep in mind this particular try one of the Platonic solids delivered prior to).

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Today look at the variety of vertices, edges and you can confronts found in our finally circle - brand new solitary triangle. You will find V=step three, E=3, and you may F=2 - we should instead however range from the exterior face. Now

In the whole process, starting with the entire polyhedron and stop that have a good triangle, the worth of V - Elizabeth + F has not altered. Anytime V - E + F = dos towards the last network, we have to supply V - E + F = dos to your polyhedron by itself! The new evidence is finished!