This reminded me of how cool the Petersen graph is; a 6-post 🧵. First, what is it? The vertices are labeled by the 2-element subsets of {1,...,5}, and there is an edge between two vertices if the subsets are disjoint. This gives S5 in its automorphism group; in fact that's all there is. #MathSky

The Petersen Graph (automorphism group: S5) showing symmetries of order 5 and 3. #GraphAutomorphisms #GraphTheory

Visualising order-3 and order-4 automorphisms in the 5-cell #GraphAutomorphisms #MathSky

Take vertices as 3-subsets of a set of 7 elements, connect two vertices if the subsets are disjoint. Result: the odd graph O(4). Automorphism group: S7. Two drawings, one showing 7-symmetry, one showing 5-symmetry. (The second drawing can probably be done with fewer crossings... not sure tho!)

Two drawings of the Heawood graph, one showing 7-rotational symmetry and one showing 3-rotational symmetry #GraphTheory #GraphAutomorphisms #ChordalRings #SymmetricGraphs #HeawoodGraph

Another visualisation of the Order 8 automorphism of the Coxeter Graph. Orbit of vertex 0 shown in red #graphtheory #grouptheory #finitegroups #symmetry

Automorphism of order 3 in the Coxeter Graph #graphtheory #grouptheory #finitegroups #symmetry

Automorphism of order 8 in the Coxeter Graph #graphtheory #grouptheory #finitegroups #symmetry

Automorphism of order 7 in the Coxeter Graph #graphtheory #grouptheory #finitegroups #symmetry