For what it's worth, here is my take on 4D planets.
A planet is a system with several modes of rotation, the nature of this is an energy transfer so that the modes of rotation become equal by energy. For a planet in four dimensions, this means that clifford rotation applies. All stars travel on non-intersecting hedrices or 2d space, this cuts across the sky as great circles. The lines swirl across the sky, because every line must set 180° opposite.
One can make a 'universal sphere' that lies on the ground, where one stands opposite the rising of the zenith-star rising, and sets the rising of other stars accordingly. It's kind of like a compass based on the local star-risings. What it gives you is what 'trace' or great circle you are on, which appears as a point on the sphere.
The sun moves, or rather moves in the same coordinate system that the earth and the stars are still. In practice, it's like our sun moving through the stars. There is no reason to assume that the sun follows a trace or great circle on the earth, rather the zodiac or sun-risings follow a great circle that crosses the zenith traces. That is the zodiac is a small circle on the zenith-sphere.
We can assume, for no good reason, that an inclination of 23.5 degrees applies. The effect is that as follows.
The zodiac appears as a small circle at 43°S (ie 2×23.5 from the south pole), these traces represent the tropics. The 43°N represents the polar circles.
The points on the tropics, for one day of the year, the sun is over-head. We have the tropic of cancer and capricorn. In four dimensions, you have the tropic of leo, the tropic of libra, &c.
The points at the sun-pole, is a great circle, which during the day, the sun rises to a maximum height of 66.5 (90-23.5), every day of the year. It just reaches a different point in the sky every day. Now, imagine pulling this circle towards the horizon. One As one pulls it towards a point, the circle has a maximum and minimum, ie at 50°s, the circle comes within 3degrees of the zenith, and at winter, only 43-degrees into the sky.
For points in the temporate range, the circle of risings lies between the zenith and the horizon, still of 47° diam. For example, at the middle on the zenith-sphere, the sun rises as high as 45+23.5 = 68.5, and as low as 45-23.5 = 21.5.
In points in the polar region, the sun sometimes hangs on the horizon, and sometimes rises higher, but never higher than 47 degrees, and often very much lower. At the poles, it never rises more than 23.5 degrees.
Back at our zenith-sphere, we now put the zodiac, with the months &c, like you sometimes see on earth-zodiacs. Anything that has the same longitude as say Leo, would have their summer in Leo. Where the longitude is that of Taurus, the summer falls then. It's just like our N=cancer, S=capricorn, but you have a full circle, not just the opposites.
We then have
- point on zenith-circle = time of the day
- zenith-longitude = time of the year
- zenith-latitude = climate (the less the sun rises, the colder it be)
On the ground, you now have time-zones (as before), and season-zones [great circles falling on a longitude on the zenith-sphere], and climate-stripes [latitude on the zenith sphere]. The climate-lines run perpendicular to the timezone and season zones, but the other two run at angles equal to distance from the climate-line (latitude on the sphere) to the nearest pole.
How much space is in the tropics and poles. This is easy to enumerate, since this is the versine of the zenith-latitude (climate).
- Polar and Equatorial = 15.9%
- Temperate = 68.2%
None the same, the entire polar region is connected, so polar bears and penguins can live side by side.