If you attempt to tile a non-Euclidean surface with five squares meeting at each vertex:
A) you will find your efforts to be impossible.
B) you will be tiling a surface with elliptic geometry.
C) you will be tiling a surface with hyperbolic geometry.

Question

Quizplus · Accepted Answer

Tiling a non-Euclidean surface with five squares meeting at each vertex is only possible in hyperbolic geometry. In Euclidean geometry, the maximum number of squares that can meet at a vertex is four, while in elliptic geometry, only three squares can meet at a vertex. Therefore, the only possible option left is hyperbolic geometry.

If You Attempt to Tile a Non-Euclidean Surface with Five