In the previous post our explorers descended into the interior of their toroidal world. One of the most interesting oddities they face is the day/night cycle.
It's difficult to think concretely about day and night in the interior when so little sunlight reaches it, so let's exaggerate the size of the sun.
Here's a shadow illustration using a sun fifteen times the size of our own sun, which takes up about 8° in the sky, almost the size of a fist at arm's length. With a larger sun, objects have larger penumbras but smaller umbras. In this case, the umbra is short enough that the near side's shadow only covers about a third of our torus's far side, leaving the thirds above and below it with partial sunlight.
This illumination pattern gives a trip south into the interior a couple inversions of the day/night cycle. First, as explorers cross the polar rim with the sun at their backs, they cross from sunlight to shadow and trade day for night.
This isn't so different from traversing the arctic on Earth and crossing the solar terminator from the day side to the night side, but a big difference does appear half a day later when the other side of a spherical planet would be back in the sun. On our torus, half a day does put our explorers back in sunlight, but since they're in the penumbra of the sunward side, they only get partial sunlight.
The half-day shift in "daytime" happens because our explorers have gone from receiving light on the side of the torus nearest the sun to receiving more light on the side of the torus furthest from the sun.
A second half-day shift occurs as the explorers descend into the umbra.
Here, the sun is completely blocked and the primary light in the sky becomes the illuminated portion of the interior overhead. "Daytime" again occurs as our explorers rotate through the sunward side of the torus.
Thus, the sunward side's umbra is more complex, and should probably be illustrated something like the diagram below, where a portion of the inner umbra is brightened by reflected sunlight, and the part that is out of view of the reflected sunlight is brightened by the reflection of the reflected sunlight:
Depending how high our torus's albedo is, its interior serves as a bit of a reflection chamber for sunlight, which gives our explorers a couple minor episodes of jet lag.
There's one other solar inversion to consider, which we'll look at in the next post.