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".
Category:List of 2nd dimension
Category:Shape
Category:Lists