Prof. John was playing an RPG game with his students. He then shows this dice to them and says that it is a dodecahedron and we can represent its vertices and edges as a graph:


Four students come up with different observations about the dice:

Student 1 says: The planar representation of the dice graph is

Student 2 says: The planar representation of the dice graph is

Student 3 says: The graph represented by the vertices and edges of the dice is three-dimensional, therefore, not planar.

Student 4 says: The standard Euler formula only applies to planar graphs, needing to be adjusted into \(V-E+F=1\) to account for the topological change in regular polyhedra like this dice.


Which student is right?

A) Student 1.

B) Student 2.

C) Student 3.

D) Student 4.

E) None of the above.


Original idea by: Rafael Brusiquesi Martins


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