A tessellation is a pattern that completely covers a flat surface using shapes that fit together with no gaps and no overlaps.

Quick Scoop: What is a tessellation?

At its core, a tessellation (also called a tiling) is like a perfectly laid tile floor. Each shape (called a tile) touches others edge to edge, and together they cover a surface completely. The shapes can be simple polygons like squares or triangles, or more creative shapes, as long as they fit together without leaving holes.

If you can slide the pattern around and still see the same look with no gaps or overlaps, you’re probably looking at a tessellation.

Key features (in plain language)

  • Repeating pattern : The same shape or set of shapes repeats across the surface.
  • No gaps : You never see the “background” peeking through.
  • No overlaps : Shapes touch but don’t sit on top of each other.
  • Flat surface : Usually we talk about tessellations on a flat plane, like paper, walls, or floors.

A kitchen floor with square tiles, a honeycomb made of hexagons, or a wall with repeating geometric tiles are everyday examples of tessellations.

Types of tessellations (mini‑guide)

  1. Regular tessellations
    These use only one kind of regular polygon (all sides and angles equal) repeated over and over.
 * Only three shapes work for this:
   * Equilateral triangles
   * Squares
   * Regular hexagons
  1. Semi‑regular tessellations
    These combine two or more different regular polygons that meet in the same repeating pattern at each corner (vertex).
 * Example: a pattern where each corner has a hexagon and triangles around it (often written as “3.6.3.6”).
  1. Other / irregular tessellations
    • Use shapes that are not regular polygons or not all the same, as long as they still cover the plane with no gaps or overlaps.
 * Many artistic tessellations fall into this category.

Where tessellations show up

  • Math and geometry : Used to study shapes, symmetry, and how space can be filled.
  • Art and design : Seen in mosaics, wallpapers, textiles, and famous works like those of M.C. Escher.
  • Architecture : Historic sites such as Roman mosaics and Islamic geometric patterns (e.g., Alhambra in Spain) feature intricate tessellations.
  • Nature : Honeycombs, some reptile scales, and certain crystal structures form tessellation‑like patterns.

Simple way to remember it

  • Think of tessellation as: “perfect tiling” of a surface.
  • If shapes repeat, touch edge to edge, and don’t leave gaps or overlap, you’re looking at a tessellation.

TL;DR: A tessellation is a repeated pattern of shapes that completely covers a flat surface with no gaps or overlaps, like a flawless tile floor or a honeycomb.

Information gathered from public forums or data available on the internet and portrayed here.