## $\text{Hexacode graph}$

This is the incidence graph of the unique symmetric transversal design $\mathrm{STD}_2[6;3]$.

 Number of vertices: $36$ Diameter: $4$ Intersection array: $\{6,5,4,1;1,2,5,6\}$ Spectrum: $6^1 (\sqrt{6})^{12} 0^{10} (-\sqrt{6})^{12} (-6)^1$ Automorphism group: $3\cdot S_6.2$ Distance-transitive: $\text{Yes}$ Bipartite, Antipodal