A configuration is polycyclic if it has a nonidentity automorphism such that the cyclic
group it generates has a semiregular group
action on the points and lines, so that all point and line orbits
have the same size. If the automorphism has order 
, the configuration is called 
-cyclic (Boben and Pisanski 2003).
Equivalently, the Levi graph of a polycyclic configuration has an automorphism whose cyclic group acts semiregularly and preserves the two parts of its bipartition. For a geometric configuration, the term polycyclic means that the orbits of the points and lines under the maximal group of rotational symmetries all have the same size; these orbits are called its symmetry classes (Berman et al. 2024).
Some named geometric polycyclic configurations, including the Berman configurations, are summarized below. The rotational order is the common size of the point and line orbits in the displayed realization (Berman et al. 2024, 2025).
| configuration | parameters | rotational order | self-dual |
| Grünbaum-Rigby configuration |  | 7 | yes |
| Berman-Gévay-Pisanski configuration |  | 3 | yes |
| Gray configuration |  | 3 | no |
| Berman configurations |  ,
 | 12 | yes |
The Grünbaum-Rigby configuration and Berman-Gévay-Pisanski
configuration are exactly the two geometric polycyclic 
configurations. There are 17 combinatorial polycyclic 
configurations (Berman et al. 2024). The
Berman 485 and 966 configurations are 12-cyclic in the
realizations summarized here (Berman 2014, Pegg 2023).
) Polycyclic Configuration." Electron. J. Combin. 31,
#P4.54, 2024.