Miquel configuration

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Miquel configuration Miquel isometric.svg
Miquel configuration
The Levi graph of the configuration is a rhombic dodecahedral graph. It is shown here with 6 red vertices from the configuration circles, and 8 blue vertices from the configuration points. Rhombic dodecahedral graph.svg
The Levi graph of the configuration is a rhombic dodecahedral graph. It is shown here with 6 red vertices from the configuration circles, and 8 blue vertices from the configuration points.

In geometry, the Miquel configuration is a configuration of eight points and six circles in the Euclidean plane, (83 64), with four points per circle and three circles through each point. It has 12 pairs of circles that share two points. [1]

Its Levi graph is the rhombic dodecahedral graph, the skeleton of both rhombic dodecahedron and Bilinski dodecahedron. The configuration is related to Miquel's theorem.

References

  1. Grünbaum, Branko (2009), Configurations of points and lines, Graduate Studies in Mathematics, vol. 103, Providence, RI: American Mathematical Society, p. xiv+399, ISBN   978-0-8218-4308-6, MR   2510707 .