There are not many sources I can read to know about this kind of Antenna and its Applications
The introduction to the 1967 NASA Goddard The Canted Turnstile as a Omnidirectional Spacecraft Antenna System says
Spin stabilized satellites will usually require an omnidirectional type antenna system since their aspect is continually changing as viewed from earth. The turnstile antenna or a variation of it is a simple, practical, system for this purpose.
and goes on to say:
The normal turnstile antenna consists of two half wave length dipoles mounted at right angles to each other. [...] The dipole pairs are excited such that they are phased 90 electrical degrees apart.
The flat turnstile antenna radiates circular polarization along the 6 axis. The sense of the circularity is opposite along the θ = 0° axis to that along the θ = 180° axis. Moving from the point θ = 0° toward θ = 90° the polarization becomes elliptical with its limit as linear polarization lying in the θ = 90° plane. The polarization would then become elliptical of the opposite sense and become circular at θ = 180°.
So this would be in the shape of a cross or X, and because the antenna are phased by 90 degrees as well as perpendicular, they can radiate or receive signal in all directions. It is a truly omnidirectional antenna, though the polarization state changes from right-hand circular polarization to linear, to left-hand circular polarization as the direction changes, but there are no absolute nulls with zero power.
That would look (a bit) like this:
It goes on to say:
The canted turnstile is formed from four monopole antennas approximately one quarter wavelength long. The bases of the antennas are usually separated by some distance (d) and the antennas are tilted at an angle (a) to the plane containing the bases (Figure 3)
Reasons for Using the Canted Turnstile Antenna on a Spacecraft:
Usually a spacecraft structure is comparatively large in terms of the wavelength used. This forces a separation of the bases of the monopoles. By using a canted turnstile on a flat surface symmetric to the spin axis the base separation may be minimized. This will usually provide much better coverage and a smoother pattern as the satellite rotates.
The canted type antenna will also fit into most vehicle shroud compartments without folding. This increases the reliability of the system.
A product description from GOM Space showing uniformity with a range of only +1.6 dBi to -1 dBi:
The turnstile antenna consists of four monopole antennas combined in a phasing network in order to form a single circular polarized antenna. The antenna pattern is almost omnidirectional and there are no blind spots which can cause fading with tumbling satellites.
The antennas are compatible with other vendor's structures and can be mounted on either the top or bottom panel of the nanosatellite. The antenna PCB is designed to be the least obstructive to any top or bottom mounted payload or panels. It has a low profile that allows a solar panel to be mounted on top, and a large diameter hole in the middle for a camera lens or similar.
Here are some radiation patterns that I found in a quick search. No affiliation, etc. While the shapes may look very lumpy, the range is only +1.6 dBi to -1 dBi.
below: Screen shots from their product brochure NanoCom ANT430 Datasheet 70 cm band cubesat antenna - Omnidirectional UHF antenna for pico satellites.