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 a semiregular automorphism that 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).
The Grünbaum-Rigby configuration and Berman-Gévay-Pisanski
configuration are the two geometric polycyclic 
configurations (Berman et al. 2024).
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Polycyclic Configuration." Electron. J. Combin. 31, #P4.54, 2024.