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Formalhaut
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Two circles with different degree of rotation in a puzzle that is still doctrinaire.

Fomalhaut, also designated Alpha Piscis Austrini (? Piscis Austrini, abbreviated Alpha PsA, ? PsA) is the brightest star in the constellation of Piscis Austrinus and one of the brightest stars in the sky. It is a class A star on the main sequence approximately 25 light-years from the Sun. Fomalhaut, K-type main-sequence star TW Piscis Austrini, and M-type, red dwarf star LP 876-10 constitute a triple system, even though the companions are separated by several degrees.
The star's traditional name derives from Fom al-Haut from scientific Arabic ?? ????? fam al-??t (al-jan?b?) "the mouth of the [Southern] Fish" (literally, "mouth of the whale"), a translation of how Ptolemy labeled it.

Fomalhaut has had various names ascribed to it through time, and has been recognized by many cultures of the northern hemisphere, including the Arabs, Persians, and Chinese. It marked the solstice in 2500 BC. It was also a marker for the worship of Demeter in Eleusis.
It was called Hastorang by the Persians, one of the four "royal stars".
The Latin names are ?s piscis mer?di?ni, ?s piscis mer?dion?lis, ?s piscis notii "the mouth of the Southern Fish".

In Walter Tevis' novel Steps of the Sun, Fomalhaut is visited by the protagonist, and two potentially inhabitable planets are found (and described). Parts of Philip K Dick's novel Lies, Inc (originally titled The Unteleported Man) are set on the fictional planet Fomalhaut IX. Ursula K. Le Guin's first novel Rocannon's World is also set on a fictional planet in the Fomalhaut system.

The puzzle itself consists of two intersecting circles. One rotates sixfold, one fivefold. Despite this and despite the very big area of intersection the puzzle is doctrinaire.

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