This is the Avanti Moonraker 4 and the similar Wilson Shooting Star. These both were combination yagi/quad directional beam antennas. The driven and director elements were yagi, while the reflector was quad. This antenna was spec'd to have a 14.5 dbi gain and 38 db front to side rejection. Sporting a 16 foot boom, and twin sets of four elements for both horizontal and vertical polarizations, this was not an antenna for the weak at heart (or more accurately, the weak of mast). With a weight of nearly 25 lbs, and a wind load of over 5 sq. feet, you had to mount it on some serious thick pipe or a tower, and only a heavy duty rotator would be up to the task of turning (and holding) this antenna in any given direction.
Because of the quad reflector you had to be very careful, when assembling this antenna, to get the wire dimensions as exact as possible, or rejection performance would suffer. There were also some radio snake oil salesmen who tried to market "rejection improvers", which were nothing more than a second wire to round the elements. These would not work, as the smaller size became resonant at a much higher frequency. But some people bought into the notion that you could "improve" the performance of this already popular antenna.
Despite the tall order (and cost) to erect and maintain such a beast, there were a few people in the local area who owned these antennas. In my area, Bedbug, Gretchen, Kenny, Wildcat, Super Plater, Cliff, and others owned either the 'raker 4 or a Shooting Star. Cliff actually had the mast come down through the roof, and into his radio room, and he turned it by hand!