The Vertex is where the prime vertical, the great circle running through the east and west points of the horizon and the zenith, cuts the ecliptic in the west. There is a compact way to compute it that also explains its behaviour: the Vertex is the ascendant calculated for the co-latitude, that is, for 90 degrees minus the geographic latitude of the birthplace, taken in the opposite hemisphere.
That identity has consequences. A chart cast at 50 degrees north has a Vertex behaving like an ascendant at 40 degrees, and one cast at 20 degrees north has a Vertex behaving like an ascendant at 70 degrees, with all the extreme unevenness of rate that a high latitude ascendant carries. Towards the equator the co-latitude approaches 90 degrees and the computation degenerates, so the Vertex becomes unstable and then meaningless for births within the tropics. Software that reports one anyway is reporting an artefact.
Its rate is otherwise a full circuit in a sidereal day, so it is as time-sensitive as the ascendant and rather more location-sensitive, which is the point the existing article makes about people born at the same moment in different places.
Two names collide here and the atlas holds both. This Vertex is a calculated point of the twentieth century. Vertex is also the traditional name of a fixed star position associated with the Andromeda Galaxy, which has nothing to do with it.