This is an antipodal 3-cover of the Berlekamp–van Lint–Seidel graph.
| Number of vertices: | $729$ |
| Diameter: | $5$ |
| Intersection array: | $\{22,20,18,2,1;1,2,9,20,22\}$ |
| Spectrum: | $22^1 7^{132} 4^{132} (-2)^{330} (-5)^{110} (-11)^{24}$ |
| Automorphism group: | $3^6:(2\times M_{11})$ |
| Distance-transitive: | Yes |
| Antipodal |