# The Art and Math of Tiling

The main mathematical news

1985: Stein discovers the 14th typeof pentagon that tiles the plane.

2015: Mann, McLoud, & VonDerauthe discover the 15th type of pentagon that tiles the plane

2017: Rao shows, using a computer, that there are no more than 15 types of pentagons that tile the plane.

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Additional Theorems / conjectures / Open questions

In how many ways can we tile the plane by polygons, vertex-to-vertex and edge-to-edge, without gaps and overlaps?

Kepler: There are 11 ways to tile the plane with regular polygons – three by using the same one polygon, and eight by using several polygons, all having the same tiling verticies.

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The main mathematical concepts / Principles

Plane Geometry (MSC2010#97G40)

*   Regular polygons

*   Symmetry

*   Tiling

*   Plane

*   Angle, Vertex, Edge,Tiling vertex

*   Convex polygon

*   Reflection

*   Translation

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