You claim symmetry as a nice feature of your avatars, yet they only have one line of symmetry. Mine has three lines of symmetry as depicted, and from any vertex of the Petersen Graph, as pictured in my avatar, the view is effectively the same. It is a 3-regular graph of girth 5 and depicts the smallest bridgeless 3-regular graph that has no 3 edge coloring. That is, you need 4 colors to color each edges such that no two colors share a vertex. Additionally, it has many varied, interesting forms, of which include the unit graph version, pictured
here. There are also other such variations in its presentation, such as the following
depiction. Note how it continues to have so many symmetries no matter the way it is presented. It is an impressive graph that is instrumental in many contradictions of postulates and ideas in graph theory and has an entire book devoted to it. Clearly, it is the superior avatar.
