I write—though not very successfully.
I wanted a chess variant in one of my stories, where the game surface is on a virtual sphere—no supplemental views or note-taking allowed. The Sphere is rolled about virtually and a big part of the difficulty is remembering and picturing the hemisphere that you cannot see.
By the way, it's called "Sphess" for "Spherical Chess."
Except the "Squares" at the very top are triangles.
Looking at the diagram, it seems that what I want is physically impossible. As the squares shrink towards the pole, eventually we are forced to a point.
I think a better question might be...
Can we imagine a bunch of four-sided figures connected topologically like the squares in a round chessboard—but in every direction?
And can we further write a program to show Half of this surface on a monitor at one time, in the shape of a hemisphere?
We literally can't have a Sphess board in the material world because it isn't physically possible in 3-D...