So I did the calculations for height of the sun in the sky at various locations on the planet. The periods of rotation were different between two planes, the wx plane and the yz plane, with one being four times that of the other.
Conceptually the run rotates around the Earth during the year. I chose the wz plane for the plane of this rotation.
I placed the sun 23.26 degrees north of the equator in the wzplane. Then rotated the sun around the planet with the rotation matrix
| cos(u) -sin(u) 0 0 |
| sin(u) cos(u) 0 0 |
| 0 0 cos(u) -sin(u) |
| 0 0 sin(u) cos(u) |
Next did the same with sun initially 23.26 degrees south of the equator. The results were quite different. In one case the wx rotation dominates, in the other the yz rotation.
The cycle of seasons lasts half of the year. That it, the planet goes through the cycle of seasons twice in one year. I suspected as much, but it is nice to see it confirmed. The two cycles are slightly different, but this might be insignificant.
The reason I suspected this is that after half a year the Sun is over the antipode of the place it began. The antipode is at the same latitude as the original location. So the season should be more or less the same every half year.
One of the poles is hotter than the other, though not greatly so. I suppose that if the obliquity of the ecliptic were zero they would be the same. The climate seems to be temperate everywhere. The length of days doesn't change at the poles. They are moving in great circles, so that makes sense.
To truly get the answer it would be necessary to do integration to see how much solar energy a spot gets during a certain time. This is kind of unusual because it's necessary to truncate the integration of the dot product. A spot gets zero energy during the night, not negative energy. So this will have to wait until I get a more powerful mathematical tool.
But I find the details unpredictable. I can't imagine the geometry.