The Pagoda antenna is an omnidirectional circularly polarized antenna design that Marteen created. His main design goals were: Good omnidirectional radiation pattern. Good axial ratio. Reasonably small. Easy to manufacture within fine tolerances at low cost, even for a hobbyist.
Pattern For comparison, here's a simulation of the traditional cloverleaf antenna using the same simulation software and setup:
The 'best case' and 'worst case' correspond to different assumptions about what happens to signals that travel along the outside of the coax. In the 'best case' simulation, these are completely absorbed at the other end of the coax. In the 'worst case' simulation, they are completely reflected back towards the antenna. The latter case usually results in standing waves on the outside of the coax, which causes the coax itself to radiate and interfere with the radiation pattern of the antenna. This is why the radiation pattern isn't smooth anymore. The reality will be somewhere between these two extremes.