Astronomicon, Book I

A circular astrological diagram illustrating hexagonal aspects (sextiles) between the signs of the zodiac. The signs are arranged counter-clockwise around the circle: Cancer (♋) at the top, followed by Gemini (♊), Taurus (♉), Aries (♈), Pisces (♓), Aquarius (♒), Capricorn (♑) at the bottom, Sagittarius (♐), Scorpio (♏), Libra (♎), Virgo (♍), and Leo (♌). Two interlaced hexagons are formed by lines connecting every other sign. A small number "1" is marked on the line connecting Aries and Aquarius, and a small number "2" is marked on the line connecting Gemini and Aries.

Some astrologers, as I said above, ignore the hexagon, and some even of those who mention it declare it to have little efficacy, as does Manilius himself and the authors whom I cite in the note to verse 358. But, like the trigon, it is held to be harmonious by Firmicus II 22 7 "hexagons are the same thing as trigons, except that they are of lesser power," Ptol. tetr. p. 9u., Hermipp. I 19, C.C.A.G. VIII ii p. 74 18. The scholiast at Paul. Alex. D 4 asserts however that this relationship is good only between Gemini and Leo, between Sagittarius and Aquarius, between Virgo and Scorpius, and between Pisces and Taurus, that is between signs which see or hear one another,—a form of intercourse to which we shall come at verse 485. Manilius himself at II 572 sq. speaks worse of the hexagon: "mostly they remain enemies, every third one by law, fixed in a transverse gaze of malice."

385–389
391–394

There might be formed a dodecagon by drawing a straight line from each sign to its next neighbour, but the efficacy of this aspect is null. Null also are the relations of signs divided from one another by four intervening signs, since the line which joins them is not the side of any equilateral figure which can be inscribed in the circle. Thus, if a line be drawn from Aries to Virgo, a line of equal length, 150°, can be drawn from Virgo to Aquarius, but a third line, drawn from Aquarius, must end at Aries, and will therefore contain only 60°, so that the figure formed will be an isosceles triangle.

Paul. Alex. E 2 "The relationship of signs that are unconnected with one another has the interval of two, six, eight, and twelve in number, and those signs that have taken on the number of this interval are also said to be averted from one another."