Tiling

A tiling (or sometimes called as a "tessellation") is the covering of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps. They can also be generalized into higher dimensions, just like polytopes.

Euclidean Tilings
Below are quick definitions of the 3 possible euclidean one-polygon 2-dimensional tilings.

Triangular Tiling
Triangular tiling is a plane filled with triangles. It has the Schläfli symbol {3, 6} and is the dual of the hexagonal tiling.

Square Tiling
Square tiling is a plane filled with squares. It has the Schläfli symbol {4, 4}.

Hexagonal Tiling
Hexagonal tiling is one of the three regular tilings of the plane and consists of an infinite number of hexagons. It has a Schläfli symbol of {6, 3}, meaning that it has three hexagons located around each vertex.

Spherical Tilings
Regular spherical tilings are just the Platonic Solids.

Hyperbolic Tilings
There are an infinite amount of regular Hyperbolic Tilings, because these are the tilings that are not euclidean or spherical.

Order-5 square tiling
The Order-5 square tiling has a Schläfli symbol of {4, 5}. It can be thought of as a "hyperbolic cube".

Order-3 heptagonal tiling
The Order-3 heptagonal tiling has a Schäfli symbol of {7, 3}. It can be thought of as a "hyperbolic dodecahedron".