Grünbaum-Rigby configuration

The Grünbaum-Rigby configuration is an exotic polygonoid. It has 21 edges of three different lengths, with 2 of each of two of the lengths at a vertex making a tetrad vertex figure. It is however regular if you consider conjugacies along with its other symmetries.

It is the simplest polygonoid with 4 vertices to every edge and 4 edges to every vertex.