Definition

1. Verb (transitive):

   • To cover a surface completely with a pattern of small, flat shapes (tiles, stones, etc.) that fit together without gaps or overlaps. This often involves using pieces of multiple colors or materials to create a decorative mosaic.
   • In geometry and computing, to subdivide a surface into smaller, repeated shapes.

2. Verb (intransitive):

   • (Of identical shapes) to fit together perfectly on a flat surface without leaving any gaps. This describes an inherent property of a shape.

Usage and Examples

• Transitive verb (to cover a surface):

  • The artist plans to tessellate the courtyard floor with hand-painted ceramic tiles.
  • Ancient Romans would tessellate their villas with intricate stone mosaics.

• Intransitive verb (to fit together):

  • Regular hexagons can tessellate a plane.
  • These puzzle pieces are designed to tessellate seamlessly.

Advanced Usage

• In Computer Graphics: The process of breaking down a complex surface (like a 3D model) into a mesh of polygons (often triangles or quadrilaterals) is called tessellation.

  • The graphics card uses a dedicated processor to tessellate the terrain, creating a more detailed and realistic surface.

• In Biology: Describing patterns in nature where cells, scales, or other structures fit together.

  • The epidermal cells of a plant leaf tessellate, forming a protective layer without intercellular spaces.

Variants and Related Words

• Tessellation (noun): The pattern or the act of tessellating.

  • The tessellation on the mosque's dome was a masterpiece of Islamic art.
  • Studying the tessellation properties of different polygons is a common geometry exercise.

• Tessellated (adjective): Having a checkered or mosaic pattern; covered with a tessellation.

  • They walked across the tessellated pavement of the ancient forum.

Synonyms

• Tile (verb): To cover with tiles (a more common, less specific synonym for the transitive sense).
• Mosaic (verb): To decorate with a mosaic (implies artistic design with varied colors/materials).
• Pave (verb): To cover a surface, typically with stone or concrete (broader, does not imply a repeating pattern of identical shapes).

Related Concepts

• Tiling: A general mathematical term for covering a plane with shapes. All tessellations are tilings, but not all tilings use shapes that fit together in the perfectly interlocking way described by "tessellate" (intransitive).
• Regular Tessellation: A pattern made by repeating a single, regular polygon (only equilateral triangles, squares, and regular hexagons can do this on a flat plane).

Verb

1. tile with tesserae
   • tessellate the kitchen floor
2. fit together exactly, of identical shapes
   • triangles tessellate