Remember the graph paper you used at school,the kind that's covered with tiny squares? It's the perfect illustration of what mathematicians call a "periodic tiling of space", with shapes covering an entire area with no overlap or gap. whether we moved the whole pattern by the length of a tile (translated it) or rotated it by 90 degrees, and we will catch the same pattern. That's because in this case,the whole tiling has the same symmetry as a single tile. But imagine tiling a bathroom with pentagons instead of squares – it's impossible, because the pentagons won't fit together without leaving gaps or overlapping one another.
Source: phys.org