Graph Theory Lessons

Lesson 6: Platonic Graphs

The Platonic Graphs are the graphs formed by the edges and vertices of the five regular Platonic solids (Tetrahedron, Cube, Octahedron, Icosahedron and Dodecahedron). To get the Platonic Graphs click Graph then Platonic and then choose the graph you want. If, for instance, you select the Cube, you will have the choice of a planar depiction or a non-planar one. Depending which you choose you will get figure 8 or figure 9.

Fig. 8, A non-planar depiction of a cube

Fig. 9, A planar depiction of a cube

Of course the two graphs are isomorphic. All the platonic graphs are planar. If you like animation save the planar depiction and then get the non planar one and click Relations and Isomorphism like you did in exercise 3.

For each of the five platonic graphs answer the following question: Is it a regular graph? If so, regular of which degree?
Which of the Platonic graphs is a complete graph?

Answers

e-mail: C. Mawata