There is a unique symmetric transversal design $\mathrm{STD}_4[12;3]$, as shown by C. Suetake (Designs, Codes and Cryptography 37 (2005), 293–304). Therefore, we introduce the name "Suetake graph" to refer to its incidence graph.
| Number of vertices: | $72$ |
| Diameter: | $4$ |
| Intersection array: | $\{12,11,8,1;1,4,11,12\}$ |
| Spectrum: | $12^1 (2\sqrt{3})^{24} 0^{22} (-2\sqrt{3})^{24} (-12)^1$ |
| Automorphism group: | $\text{Has order }2^6\cdot 3^3=1728$ |
| Distance-transitive: | $\text{No}$ |
| Bipartite, Antipodal |