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{\bf Marko Boben, \v{S}tefko Miklavi\v{c} and Primo\v{z} Poto\v{c}nik}
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{\bf Rotary Polygons in Configurations}
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A polygon $A$ in a configuration $\mathcal{C}$ is called rotary if
$\mathcal{C}$ admits an automorphism which acts upon $A$ as a one-step
rotation.  We study rotary polygons and their orbits under the group
of automorphisms (and antimorphisms) of $\mathcal{C}$.  We determine
the number of such orbits for several symmetry types of rotary
polygons in the case when $\mathcal{C}$ is flag-transitive. As an
example, we provide tables of flag-transitive $(v_3)$ and $(v_4)$
configurations of small order containing information on the number and
symmetry types of corresponding rotary polygons.

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