Tessellations

Math test 9/26/25

Tessellation

A repeating pattern of shapes that fit together with no gaps or overlaps.

M.C. Escher

M.C. Escher was a Dutch graphic artist famous for impossible shapes and tessellations.

Graphic Art

Graphic art is art made with lines, shapes, and patterns; often prints or drawings. Also used in video games.

History of Tessellations

Tessellations have been used for thousands of years in mosaics, Islamic tiles, and in nature like honeycombs.

What inspired Escher?

Moorish tile designs from Spain inspired Escher’s tessellations.

Math used in tessellations

Geometry, including shapes, angles, symmetry, rotation, reflection, and translation.

Monohedral tessellation

A tessellation using only one type of shape.

Regular tessellation

Made with one type of regular polygon repeated to cover a plane.

Irregular tessellation

Made with different shapes or polygons that don’t have equal sides or angles.

Semi-regular tessellation

Combines two or more types of regular polygons in a repeating pattern.

Shapes that can make regular tessellations

Triangle, square, hexagon.

Shapes that cannot tessellate

Pentagons, heptagons, or shapes whose angles don’t divide 360°.

Vertex, edge, angle

Vertex = corner; Edge = side; Angle = space between edges at a corner.

Angle sum needed for tessellation

Angles around a vertex must add up to 360°.

Examples in everyday life

Floor tiles, brick walls, honeycombs, computer graphics, fabrics.

Tessellations in gaming

Used for tile-based maps, textures, and level design.

Careers that use tessellations

Architects, graphic designers, game designers, textile designers, engineers.

Tessellations in architecture

Patterns in floors, walls, facades, ceilings for style and efficiency.

Tessellations in manufacturing

Efficient cutting, packing, and pattern design with minimal waste.

Tessellations in fashion/textiles

Repeating patterns for clothing, fabrics, and prints.

Tessellations in computer graphics

Algorithms create textures, 3D models, and animations efficiently.

Tessellations in puzzles/education

Used in brain teasers, math games, and learning tools for patterns and geometry.