Explore regular tiling patterns and symmetry in geometry.
Pattern Controls
Notice how the total angle at any vertex always equals 360 degrees. This is why other shapes like pentagons cannot tile the plane regularly.
Pattern Analysis
Internal Angle90°
Vertex Sum360°
4 × 90° = 360°
Regular square Tiling
About this calculator
What is Tessellation?
Tessellation is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellations can be generalized to higher dimensions and a variety of geometries. Regular tessellations use only one type of regular polygon.
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Pro Tips
Only three regular polygons can form a regular tessellation by themselves: triangles, squares, and hexagons.
The internal angle of a regular n-gon is (n-2)×180/n.
Tessellations are found everywhere in nature, like honeycombs and snake skin.
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Fun Facts
"The artist M.C. Escher is famous for his incredible and mind-bending tessellated artworks."
"The term 'tessellation' comes from 'tessella', the small square stones used in Roman mosaics."
"Aperiodic tessellations (like Penrose tiling) never repeat their pattern perfectly no matter how large the area."
