Is A 2-Sided Polygon Possible?

65, 4, 3, 2, 1. Why don't we ever learn about dgon and monogon? Well, it's because they're impossible, right? No real eyes realize that you and I walk around on Dion and monagons every day. But big flat tells us that two straight lines can only meet at no points, one point, or every point.

A Dion, a polygon where two straight lines meet at two points, that could only happen if the lines curve. Then, it wouldn't be a polygon. But what if the lines don't curve? What if instead the space they inhabit curves? This line is straight. A two-dimensional observer would agree that it never turns, but unbeknownst to them, the line does curve into a higher spatial dimension beyond their comprehension.

Add another straight line sharing those vertices, and you've got a spherical loon, and it's a true two-sided polygon. But it's only possible in spherical geometry. On top of that, the hemisphere you live on is a monogon, a one-sided polygon. Its one and only side is any spherically straight line you can draw on the globe: a great circle.