I found this which might help, but the whole thing looks kinda slap-dash - I don't think there was any real thought involed at all...
Quadrant Stuff
Or there's the official explaination:
Quadrant Stuff
Or there's the official explaination:
Does that help?
An astrographic organization al system devised for the Milky Way Galaxy by the UFP and the major neighboring stellar governments, using once again the alphabet of Earth's ancient Greeks. The quadrants make up one-fourth each of the great plane of the galaxy when viewed from "above" as a circle or clockface. Using the imaginary axis drawn through the galactic center, the first boundary of the four 90-degree "crosshairs" is defined as a line drawn from the axis outward through the Sol system, widened into a full plane perpendicular to the galactic equator. The resulting configuration, when viewed as a 20th century Terran clockface, leaves the Alpha Quadrant lying between "6 o'clock" and "9 o'clock," the Beta between 3 and 6, the Gamma between 9 and 12, and the Delta from 12 to 3. Federation science knows the most about its home quadrant, Alpha, with Gamma and Delta the least known -- until the opening of the Bajoran wormhole to the former and the once-lost U.S.S. Voyager's mission logs about the latter.