It's been a while, forgive me if I blow a few of the terms....
I'm not sure what you're referring to when you say "Planes," I think it's what we used to call "fronts,"like a "voltage" and "current" or E and I front...something like that...The antenna is not omnidirectional, the best gain is from the end, like a yagi.
The antennas are twisted to accomodate the rotational polarity of the inbound signal (left or right -hand circular polarity). Using a horizontally or vertically polorized antenna for circular polorized signals results in a drop of (I believe) ~3dbd. Using a circ polorized antenna for horizontal or vertically polorized signals has about the same drop, but offers some resistance to many of the various kinds of fading and terrestrial noise effects.
The same rotational polarity can be achieved by feeding an array of dipoles, staggered horizontally and vertically, either a half or quarter wave apart (don't remember)..I think it's a quarter wave.
I used to work the amateur radio satellites (VHF/UHF) with a pair of KLH beams on an Az/El rotator (which was controlled by the computer using a KC tracker). The VHF beam was a 20 element, the UHF was a 40 element. Both had switching for L/R CP. Another guy in the neighborhood made some QFH antennas and swore by 'em as the queitest antennas he'd ever used (terrestrial noise rejection).
If I'm remembering correctly, rotational polarity is preferred for "space work," even though it has more loss / less gain, because it penetrates the atmosphere with less distortion.
The Amateur Radio Relay League (ARRL - arrl.org) has some pretty good antenna books. I used to have one that included QFH antennas, and the formulas to get the twist ratio, overall length, etc.....if you can get you hands on one of those books, perhaps the explaination will give you more helpful/specific information.
FWIW
Scott