I can imagine it. You just have to embed it in a non-Euclidean geometry. A great circle can be constructed from 4 straight lines, and thus is a square, and it still has every point at a fixed distance from a common center (okay, 2 common centers), and thus is a circle.

Alice laughed. 'There's no use trying,' she said. 'One can't believe impossible things.'

I daresay you haven't had much practice,' said the Queen. 'When I was your age, I always did it for half-an-hour a day. Why, sometimes I've believed as many as six impossible things before breakfast. There goes the shawl again!

― Lewis Carroll

See also this article discussing the usefulness of believing impossible things.