Isometric Miquel Configurations of Points and Circles

Abstract

Summary The classical six circle theorem of Miquel gives rise to a configuration consisting of eight points and six circles. We prove that this configuration can be realized by circles of equal size. Moreover, if five of the circles have unit radius, then the sixth circle must also have unit radius. In the proof, we use the Levi graph of this configuration, which is isomorphic to the skeleton of the rhombic dodecahedron.