WhiteTower: Yes, the Earth is spherical in the relevant sense. But the point is that the playing area of the game called "Sphere" Froglet is not equivalent to a sphere. Look at a map of the Earth. Yes, the east and west edges should be joined together, but not the north and south edges. Or are you really suggesting that Greenland is adjacent to Antarctica?

Or look at it another way. Start with a rectangular piece of paper, and think of it as representing the board in the standard Froglet game. Now the rules for "Sphere" Froglet tell us that the left and right edges should be joined, and the top and bottom edges should be joined. So take the paper and first join the left and right edges. We now have a cylindrical tube. Then if we join the top and bottom edges (this may require the paper to be a bit stretchy) we have something in the shape of a doughnut, which is called a torus. The name is not what's important here, and in my view Doughnut Froglet would be as good a name as Torus Froglet. The point is that it is in no way equivalent to a sphere, and hence "Sphere" Froglet is a misnomer.

alanback: You and others have used the phrase "mathematical correctness" (or "mathematically correct") as if the word "mathematical" somehow means that correctness is of no importance. It seems to me that when we have a choice between correctness and incorrectness, we should choose correctness. Why should it matter whether it's mathematical, topological, topographical, geographical, geological, biological, anthropological, etymological, or entomological?